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Effects of Scatter Subtraction on Detection and Quantitation in

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					Effects of Scatter Subtraction on Detection and
Quantitation in Hepatic SPECT
Daniel J. de Vries, Michael A. King, Edward J. Soares, Benjamin MW. Tsui and Charles E. Metz

Department ofNuclear Medicine, University ofMassachusetts         Medical School, Worcester; Department ofMathematics,               College of the
                     Massachusetts; Department ofBiomedical Engineering and Department ofRadiology, University of North
Holy Cross, Worcester@
Carolina at Chapel Hill, Chapel Hill, North Carolina; and Department ofRadiology,           University ofChicago Medical Center@
Chicago, illinois


                                                                tion of scattered photons from primary (i.e., nonscattered)
The purpose of this investigation was to examine the effects of photons using a conventional Nal gamma camera.
subtractivescattercompensation     methodson lesiondetection       Various methods have been proposed to compensate for
and quantitation. Methods: Receiver operating characteristic    the adverse effects of scatter, and most evaluations have
(ROC) methodology was used to measure human observer focused on measures of the fidelity of image pixel values and
detectionaccuracy  fortumorsintheliverusingsynthetic  images.
                                                                        quantitative       accuracy.   Several     reviews     and     comparative
           R
Furthermore, OC resultswere comparedwith mathematical
models for detection and activity quantitationto examine (a) the        assessments of some of these methods have been presented
         f            humanperformance (b) the relation
potential or predicting                      and                        (1—5).
ship between the detection and quantitationtasks. Images with             A common strategy used for scatter compensation in
both low and high amounts of scatter were compared with the             volves the subtraction of an estimate of the scatter within the
ideal case of images of primary photons only (i.e., perfect scatter     photopeak       energy    window     from the photopeak         image. The
rejection) and with images corrected by subtracting a scatter
                                                                  assumption is that scatter represents an error with respect to
image estimated by the dual photopeak window method. Re
suIts: Withlowcontrast umorsin a lowcountbackground,
                        t                                the      the primary image, and methods for reducing or removing
results showed that scatter subtraction improved quantitation but scatter represent an attempt to correct an image. Various
did not produce statistically significant increases in detection  methods for scatter subtraction have been proposed. Some
accuracy. However, primary images did produce some statisti       approaches use scatter images acquired outside of the
cally significant improvementsin detection accuracy when com      photopeak region of the energy spectrum to estimate the
pared with uncorrected images, particularly for high levels of scatter distribution in the photopeak image. Increased quan
scatter. Conclusion: Although scatter subtraction methods may
provide improvedactivity quantitation,they may not significantly titative accuracy and contrast were reported for the dual
improve detection for liver SPECT. The results imply that signifi window subtraction method (6), where pixels of an image
cant improvement in detection accuracy for the conditions tested  from a Compton scatter window were scaled by a factor, k,
may depend on the developmentof gamma cameraswith better and subtracted from the photopeak image. However, the
scatter rejection.                                                subtraction resulted in increased noise fluctuations, which
Key Words: lesiondetection;receiveroperatingcharacteristic gave a signal-to-noise ratio (SNR) that was comparable to
analysis; scatter correction                                      that in the uncorrected image (6). A similar method,
J NucI Med 1999;40:1011—1   023                                 proposed for obtaining accurate SPECT quantitation, was
                                                                  based on the assumption that the shape of the scatter energy
                                                                        spectrum       can be approximated       at each pixel with a triangle if
                                                                        there is a single emission peak or with a trapezoid if scatter
     cattering of photons within the patient is one of the              spills down from multiple peaks (7). By using scaled,
several sources of degradation in image quality and quantita            narrow windows abutted to either side of the photopeak
tive accuracy in SPECT. Scattered photons primarily reduce              window, the triple energy window method gives an im
contrast and also degrade spatial resolution. Quantitation is           proved estimate of the scatter distribution. However, the low
affected   by the presence     of scattered    photons     that   are   number of counts detected in the narrow windows may
mispositioned in the image with respect to the location of the          present    a disadvantage      in comparison         to the dual window
emission of the photons. The problems presented by scatter                 subtraction method (8).
are particularly important for low energies, such as those of                  Other proposed subtraction methods estimate scatter
201Tland 99mTc,where the change in energy due to Compton                   using only the data contained within the photopeak image. A
scatter is often small enough to prevent adequate discrimina               convolution-subtraction   method was proposed, which esti
                                                                           mated the scatter image by convolving a decaying exponen
   Received Feb. 19, 1998; revision accepted Jan. 12, 1999.
   Forcorrespondence   orreprints  contact: aniel . deVries,PhD,Department tial function with the photopeak image (9). Other methods
                                           D     J
of Radiology,Brigham Women's
                      &             Hospital, 5Francis
                                            7          St.,Boston, A02115. have been based on dividing the photopeak into two
                                                                 M



                                                         SCArFER SUBTRACTION IN HEPATIC SPECT                        d
                                                                                                                   • e Vries et al.           1011
subwindows, where either a direct difference of the two                   Similarly, we have shown with ROC studies that the
images was used to remove scatter from one (10, 11) or a               removal of scatter may increase the accuracy of the simple
ratio of counts in the two windows was used to subtract an             detection task only for particular conditions (19). For low
estimate of scatter from the summed subwindow images                                    tumors in synthetic hepatic SPECT images,
                                                                       contrast, “cold―
(12, 13). For any of these corrections,     a gain in contrast or in   our dual photopeak window (DPW) scatter subtraction
quantitative accuracy comes at the expense of reducing the             method (13) did not produce a statistically significant
counts in the projection images set and altering the noise             increase in detection accuracy. However, the ideal case of
characteristics   of the reconstructed    SPECT   images.              primary   images showed    significantly   higher detection   accu
   The references cited for reviews and assessments of                 racy in comparison to the uncorrected photopeak images.
scatter compensation methods provide a fairly good represen               Given that ROC experiments can be costly in terms of
tation of the means that have been used to evaluate the
                                                                       time and resources, there has been an interest in finding
methods. They include comparison of total counts in images
                                                                       ways to predict human observer performance for various
with and without correction to a reference image of the
                                                                       tasks. Based on signal detection     theory, mathematical     algo
source in air (2), spatial resolution before and after correc
                                                                       rithms have been derived to serve as “model    observers―for
tion (2) and the corrected image to a reference image using
                                                                       the assessment of image quality (20—22).These mathemati
the normalized mean square error (3,5). Additional means
                                                                       cal observers can produce task-dependent, physical SNRs
used to evaluate the methods include measurements of
lesion contrast with and without correction (2,3), calcula             based on image parameters (23,24) and have been used to
tions of SNRs using lesion contrast and the standard                   evaluate or optimize the design of imaging systems or to
deviation of counts in the background (2,4), activity recov            evaluate or predict human observer performance (25,26).
cry ratios (2,3), the root mean square of the percent relative             In the context of medical imaging, detection of a signal
error in the corrected image (5), plots of concentration ratios        (e.g., a lesion) and activity quantitation are examples of
from corrected images versus the true concentration ratios             classification and estimation tasks, respectively. Barrett (23)
(4) and plots of countsin correctedimages versusthe true               has presented several mathematical models for calculating
counts (4).                                                            figures of merit for these tasks in terms of SNRs. Further
    Given that scatter correction by any method will change            more, mathematical relations between the SNRs of several
the contrast and the magnitude and texture of noise in an              analogous pairs of classification and estimation tasks were
image, it cannot be assumed that the result will necessarily           derived (23).
provide improved detection accuracy for human observers.                   With a need for additional information regarding the
A thorough examination of the effect of scatter correction             effect and utility of scatter correction in SPECT, we con
must include an assessment of detection accuracy. Receiver             ducted experiments that were designed to study the effects of
operating characteristic (ROC) analysis is the widely ac               scatter subtraction   on detection and quantitation. By using
cepted methodology for testing human observer detection                synthetic   images,    we intended   for the experiments    to
accuracy in medical imaging (14,15).                                   approximate clinical imaging conditions, while isolating the
   ROC analysis was used in a study that had implications effects of scatter subtraction. The effects on the simple
for the effect of scatter on detection in planar images (16).          detection task were evaluated with human observers using
Rolland et al. (16) evaluated the effect on detection of                                        d
                                                                       ROC analysis. Furthermore, etection andquantitationwere
deconvolution filtering of long-tailed point spread functions,         evaluated with one pair of analogous mathematical models.
which can arise from physical processes such as scatter. The
                                                                       The object was a focal lesion in the liver, and both cold and
authors reported significant improvement in detection accu
                                                                       hot contrasts were considered.
racy as a result of the filtering.
                                                                          For evaluation of quantitative accuracy, the region-of
    The effect of scatter reduction on detection in SPECT
                                                                       interest (ROI) estimator, although suboptimal, represents a
images was studied by Staffet al. (17), with a comparison of
                                                                       common approach to extracting quantitative information
uncorrected images with spatial filtering by the energy
                                                                       from image data (23). Counts within an ROl applied to a
weighted acquisition method (18). Three human observers
                                                                       reconstructed image are simply summed. The related detec
were required to locate and detect “cold―       lesions in a
cylindrical phantom that presented an unstructured, hot                tion model is the non-prewhitening (NPW) matched filter, a
background and in a Hoffman brain phantom. The results                 quasi-ideal model observer. Whereas the ideal observer
were pooled over observers and were analyzed with methods              detects all information needed for a given task and maxi
typically used for ROC studies of the simple detection task            mizes the sensitivity at any prescribed level of specificity
(i.e., where localization is not part of the task). Examination        (21), the accuracy    of both the human and NPW observers            is
of the ROC curves reportedly demonstrated a statistically              degraded by noise correlations (24,26), which can either
significant increase in the area under the curve for energy            mimic or mask the lesions to be detected in SPECT images.
weighted acquisition compared to no correction, but only for           We compared ROC results from human observers with the
the cases with structured background (i.e., the brain phan             results from the NPW observer and ROI estimator to
tom).                                                                  examine the potential for predicting human detection perfor


1012                   O        MEDICINE Vol. 40 • 6 •
              THEJOURNAL FNUCLEAR      •         No.   June 1999
mance and the relationship       between    the accuracy    of detec     high-count (i.e., approximately noise-free) primary SPECT images
tion and of quantitation.                                                of both contrast polarities. The locations were selected to represent
                                                                         a range of location-dependent SNRs, as measured in the projection
MATERIALS AND METHODS                                                    data by the ideal observer (19). The contrast was specified by the
                                                                         ratio:
Simulated Clinical Conditions
  Synthetic SPECT images were used for the experiments, be
cause they enabled us to determine the truth regarding the presence
                                                                                               contrast =
                                                                                                            N tmr Nivr
                                                                                                                N1@
                                                                                                                         ,                 Eq.1
of a lesion and to separate the primary and scatter components of an
image. The SIMIND Monte Carlo simulation software (27) was               where Ntmrand Nivrwere the numbers of photons emitted per voxel
used to propagate photons through a digitized, anthropomorphic                                                                        13%
                                                                         from the tumor and liver, respectively. A contrast of 13% (—
phantom obtained from CT images (28). High-count projections             for cold tumors and + 13% for hot tumors) was determined in
were produced with primary and scatter images saved separately           preliminaryexperimentsto producean appmpriatelydifficulttask (/9).
(26 millionphotons ereemitted
                     w            perSPECTprojection     set).              The simulated SPECT camera system approximated the charac
   The biodistribution of F023C5 anti-carcinoembryonic antigen           teristics of a Picker PRISM camera (Picker International,          Inc.,
(CEA) antibody fragments was approximated (29). From averaging           Cleveland, OH) with a low-energy, ultra-high-resolution (LEUHR)
over 7 patients at 3 to 5 h postinjection, the percent dose (and         parallel-hole collimator, a circular radius of rotation at 2 1.5 cm,
standard deviation) in the whole organ was 9. 1 (±2.2), 1.3 (±0.8)     9.4% FWHM energyresolutionat 140 keV, and an intrinsic
and 18.7 (±6.1) for the liver, spleen and kidneys, respectively.        resolution ofO.28-cm FWHM. With a pixel size ofO.36 cm, 128 X
Motivated by results from preliminary ROC experiments, we                128 projection images were produced at 128 viewing angles.
increased scatter into the liver region by increasing the dose in the      For both contrast polarities, five treatments of SPECT images
spleen to a level 3 SDs higher than the mean. The simulated activity     were evaluated: ideal scatter subtraction, represented by photopeak
distribution had 22.8% of the total activity in the liver, 8.8% in the   images containing only primary (i.e., nonscattered) photons; @mTc
spleen and 46.6% in the kidneys, with the remaining 21.8%                images with no scatter correction and scatter fractions typically in
distributed throughout other organs as an approximately uniform          the range of 0.4—0.5(denoted as low scatter); images of a
background. Given that the specificity of the F023C5 anti-CEA            hypothetical radioisotope with scatter fractions in the range of 1.0—
antibody fragment could result in either cold or hot tumors relative     I .2 (denoted as high scatter), which could arise from cases of
to the uptake in the normal liver, each contrast polarity was studied    multiple emission energies (e.g., 20111and WIn); and images with
in separate experiments.                                                 DPW scatter subtraction    applied to both the low- and high-scatter
  To produce images representing multiple patient cases, several         cases. The DPW method, which was being considered for clinical
locations in the liver were used for simulated tumors and multiple,      use when our initial ROC studies were being designed, was
independent Poisson noise realizations were added to the projec          selected as a clinically feasible method that was fairly representa
tion images. Tumors were represented by 2.5-cm-diameter spheres,         tive of the various energy-based, scatter subtraction methods that
a size that was considered sufficient to allow changes in contrast       use multiple energy windows to estimate scatter in the photopeak
which were produced by varying the amount of scatter—to be             region. The five treatments are listed in Table 1, with the total
perceived, even though partial volume effects could reduce the           counts in the projection sets used to obtain the SPECT images.
measured activity contrast by about 20% (30). Locations were                 Acquisition of the projection images was simulated with a 20%
selected such that the distance to any liver boundary was greater        energy window centered on 140 keV. Projections for the high
than the tumor radius plus twice the full width at half maximum          scatter conditions were produced by scaling the scatter component
(FWHM) of the camera system to avoid having a tumor easily               of the 99mTcprojections by a factor of 2.5. The DPW correction of
recognized by a change in the appearance of the edge of the liver.       projections was implemented as described by de Vries and King
(This constraint required elimination of normally cold regions,          (/3), using simulated calibration experiments. The dual windows
such as hepatic veins and arteries, and the biliary tree.) Tumor         were 5% and 15% in width and abutted at 7 keV below the
projection sets were scaled to obtain the desired contrast and were      photopeak (i.e., WL, 126—133   keV; W@, 133—154keV). The scatter
then either added to or subtracted from the liver projections to         estimate for the total 20% window was obtained from a power
produce hot or cold tumors, respectively.                                function that related the scatter-to-total count ratio (STR) in the
  The locations studied are illustrated in Figure 1, which shows         total window to the lower-to-total window count ratio. For the ith




  ‘,                           ‘5,

                                                                                                   FIGURE 1. Fromleftto right,the tumor
                                                                                                   locations that gave lowest, mid-range and
                                                                                                   highest SNRs, which were calculated us
                                                                                                   ing ideal observer applied to noise-free

  ‘,                           ‘Sb                                                             primary projection set. Arrows point to
                                                                                                   lesionfor bothcold (upperrow)and hot
                                                                                                   (lower row) contrast polarities. (Threshold
                                                                                                   ing was applied to increase the visibility.)



                                                           SCArcER SUBTRACTION IN HEPATIC SPECT                   d
                                                                                                                • e Vries et al.        1013
    pixel of the total photopeak image, the calculated STh was:         upper threshold, above which pixels values were clipped. Given the
                                                                        high activity in the spleen and kidneys, the clipping of high values
                                  I     WL[iJ     \B
@                  STR[i] = A x I@WL[i WU[i]) C,
                                          +                       Eq.2  did not occur in liver pixels.
                                                                           An image contained either one lesion or none, and the locations
    where the values of the coefficients, A, B and C, were A = 2.792,   evaluated by the observers in the lesion-present images were the
    B = 1.015andC = —0.2749 the low-scatter
                                     for                condition,and same locations evaluated in the lesion-absent images. As each
    A = 2.539, B = 0.6865 andC = —0.5486 the high-scatter image was presented sequentially,a continuousscale from “definitely
                                                    for
                                                                                to
    condition. The product of the STR and counts in the total image at absent― “definitely         was
                                                                                              present― usedtorate an observer'sconfidence
    each pixel produced the scatter estimate, which was smoothed with   regardingthe decisionaboutthe absenceorpresence ofa tumor (35).
    a Wiener low-pass filter before subtraction (13).                      For each treatment, there were 240 images for rating in the study
       The synthetic images provided the ability to increase the        sessions. These images were produced from the three tumor
    statistical power of the ROC analysis through the use of correlated locations, each having two signal conditions (i.e., present or
    images (31). For a particular tumor location and noise realization          absent) and 40 different Poisson noise realizations for each signal
    (i.e.,a “case―),
                   an image for each fl@eatment constructedby adding
                                               was                              condition. The 240 images were divided into two subsets of 120
    the appropriatescatter image to the primary image to produce tmccr          images each, with the reading order of the images in the subsets
    rectedand DPW-corieCted   imagesfor both levelsof scatter.                  randomized for each observer. The subsets for each of the five
      SPECT images (128 X 128, 0.36-cm pixels) were reconstructed               treatments were arranged in 10 study sessions, such that the subsets
    with techniques that were typically used in our clinic with                 were read in a different order by each observer.
    commercially     available    software.   Ramp-filtered    backprojection      Before each study session for a particular treatment, an observer
    was used, with noise-suppression prefiltering by a two-dimensional          was trained by first viewing the noise-free signal-present and
    Butterworth low-pass filter (order 4; cutoff frequency 0.25 cycles/         signal-absent images for each tumor location and then rating 60
    cm). The SPECT images, which contained at most one tumor, were              noisy images (10 noise realizations for each of two signal
    reconstructed through the center ofthe tumor. Multiplicative Chang          conditions at three tumor locations). When the observer entered a
    attenuation correction was applied (32), using an elliptical attenua        confidence rating, the corresponding noise-free image was dis
    tion map that approximated the cross section of the slice. The              played adjacent to the noisy image, and the observer was told
    narrow-beam attenuation coefficient at 140 keV, used by the Monte           whether or not a tumor was present. The 60 images were presented
    Carlo program (ji = —0. 546 cm'),
                            1                     was applied to primary and
                                                                                in a different order before the reading of the second subset of study
    DPW-corrected images. Effective attenuation coefficients (ps) and           images for a treatment. From this experience,          an observer was
    build-up factors (B0) for bmad-beam attenuation were calculated             expected to learn to identify lesions and to set rating strategies.
    (33) and applied to the uncorrectedimages(liE = —0.1163m@ c                 Images from each treatment were read independently by seven
    andB0 = 1.O79forlowscatter; p@= —0.0831m@ andB0 = 1.177
                                               c                                observers, who were members of the medical physics research
    for high scatter).                                                          group of the Department of Nuclear Medicine at the University of
                                                                                Massachusetts Medical School. Readings took place in a dark
    Human Observer Detection Accuracy                                           room, with no constraints on either the time allotted for reading
       The detection experiments were designed for signal-known                 images or the viewing distance. However, observers were not
    exactly (SKE) conditions, in which lesion size and shape were               allowed to change the brightness and contrast levels of the display
    constant and the location to be evaluated was indicated by cross            monitor, given that a constant transfer function for mapping
    hairs, which could be toggled on and off by the observer. Software          gray-scale pixel values to luminance was desired.
    developed at the University of North Carolina at Chapel Hill was               The transfer function of the monitor was modified with a
    used for the display and rating of images (34).                             mapping that ensured that equal steps in gray-scale values would be
       Before display, each SPECT image was magnified by a factor of            perceived as equal differences in luminance, given that the human
    3 using bilinear interpolation, and the central 256 X 256 pixel             visual system response as described by Weber's Law shows a
    region was extracted to fill an area of 25 cm2 on the display               logarithmic relationship between intensity and perceived bright
    monitor. Furthermore, each image was scaled such that the                   ness (36). The modified mapping produced the desired log-linear
    background (i.e., liver) would be displayed at nearly the same gray         transfer function and, thus, the effects of monitor characteristics on
    level for both cold and hot tumor experiments. Pixel values that            displayed contrast were reduced. The measured luminance ranged
    were negative or zero were mapped to a gray level of zero; the              from 0. 1 to 57.4 foot-lamberts (0.343—196     cd/m2). The mean
    mean liver pixel value (excluding the tumor) was mapped to the              background luminance in the liver was in the range from 3.0 to 3.5
    mid gray-scale level (out of 127 levels). The scaling determined an         foot-lamberts. To eliminate background luminance from all regions
                                                                                except the region used for reading and rating the images, we placed
                                                                                a mask on the monitor.
                                    TABLE     I                                    For each observer and treatment, a fitted ROC curve and the area
                   Treatments Studied and Count Levels                          under the curve (AUC), A5, were estimated using the LABROC1
                                                                                program (35). The average ROC curve for each treatment was
                                                              countsin          produced by averaging the curve parameters, a and b, from the
                 TreatmentTotal
         setA:Primary                                     projection            seven observers. The perceptual SNR of the human observers was
                  (ideal correction)8.77
         10@B:Uncorrected                                        X
                                                                                then calculated by converting the AUC to the detectability index,
         10@C:Uncorrected
                       low-scatter12.50                           x             d1, using the relation
         10@D:DPW-corrected
                       high-scatter21                         .82 x
         1O@E:DPW-corrected
                          low-scatter8.55                         x                                              1       1       d@
@                                high-scatter8.25                x 106                                   AUC =       +       erf -@,             Eq.3



    1014                               •        No.   June
              THEJoua@i OFNuci@i@M&ncm@ Vol. 40 • 6 • 1999
@                                         (@
      where erf(.) is the error function. The value of da was regarded as                  where g is raw image data with M pixels arranged as an M X 1
      the human observer SNR.                                                              vector, the N X 1 vector f is the discrete representation of the object
         To perform multiple comparisons of treatment SNRs while                           (i.e., the pixelized distribution of activity in the patient), H is an
      limiting type I errors (i.e., rejection of a true null hypothesis), we               M X N matrix that represents the imaging system and n is an M X
      conducted a two-way analysis of variance (ANOVA) to determine                        1 vector representing noise in the image (23). An estimate, f, of the
      whether or not there was evidence of a real, nonrandom difference                    object is obtained from g by the reconstruction process. An
      between the treatment means (averaging over observers). The null                     observer, whether human or mathematical, performs the simple
      hypothesis, H0, was that all treatments were equal, whereas the                      detection task by comparing a test statistic, X(f), to a threshold to
      alternative hypothesis, HA, was that there were real differences                     classify images as either signal present or signal absent.
      between the treatments. The null hypothesis was rejected when the                       For comparison to the human observer, the NPW observer was
      value of the calculated test statistic was greater than the critical                 implemented as a matched filter. Filters, or templates, were formed
      point of the upper 5% of the F distribution with degrees of freedom                  by reconstructing a noise-free image through the center of the
                                =
      of4 and 24, that is, F4,24 2.78 for a = 0.05.                                        tumor for each of the three locations and five treatments. The
         When the null hypothesis of the ANOVAwas rejected, Scheffé's                     appropriate template, w, was cross-correlated with the SPECT
      test for multiple paired comparisons was applied (at the 5% level)                   images, producing a linear combination of the pixel values from f.
      to examine the significance of seven differences in mean SNRs                        This value, the test statistic, is given by the weighted sum:
      between treatments: primary versus uncorrected low scatter (A                                                                                                       N
      versus B); primary versus uncorrected high scatter (A versus C);                                                                                                                                                     Eq.8
      primary versus DPW-corrected low scatter (A versus D); primary                                                                               Mo 1=1
      versus DPW-corrected high scatter (A versus E); uncorrected low                             .                      .
                                              .                                            With          w     having            the    profile   of        the      tumor,       the    highest    values    of     w     were
      scatter versus uncorrected high scatter (B versus C) DPW-                                                .   . -‘
                                                                                           placed on the locations in f where the tumor was expected to be and

@
                               .


                                          .
      corrected low scatter versus uncorrected low scatter (D versus B)
      and DPW-corrected high scatter versus uncorrected high scatter (E
      versus C). The null hypothesis for Scheffd s test was
                                                                           .


                                                                                                    fthe were
                                                                                            ofprofile. images
                                                                                           centerusing that
                                                                                             theByfor
                                                                                           the


                                                                                                      same rated
                                                                                                      values



                                                                                                                  .
                                                                                                                        of   w
                                                                                                                                . .
                                                                                                                                   decreased




                                                                                           by the human observers in the ROC expenments, the effects of
                                                                                                                                                       to
                                                                                                                                                       .
                                                                                                                                                              zero        with     increased       distance        from       the




                                                                                           scaling the images for display were taken into account.
                                    H@:            =0,
                                              @k@SNR1                              Eq. 4          With the lesion-present images having a signal in the presence of
                                                                                           noise and the lesion-absent images having only noise, the NPW
      where there were c treatments; SNR1 was the mean SNR for                             observer produced a distribution of test statistics for both signal
      treatment i (averaged over observers) and the ks were constants                      present (sp) and signal-absent (sa) images. For each of the five
      assigned the values —, 0 or + 1, which summed to zero and
                             1                                                             treatments and each lesion location, the mean and variance ofthe sp
      produced the desired differences between pairs of SNRs. The                          and sa distributions were used to calculate a physical SNR from the
      Scheffé statistic was given by
               test                                                                        detectability index, da:

                                                                                                                                                                            E
                                                                                                                                                             [E(X(f')Isp) — (X(f) Isa)]2
                                                                                                                       = d@
                                                                                                                  SNR@1@@ =                                                                                                Eq. 9
@                              5=         1—1                                                                                                                 sp)
                                                                                                                                                       ½Evar(Mf) + var(X(f) (sa)]'
                                                                                   Eq.5
                                                                                           where the number of sp and sa images for a given tumor location
                                     (c —l)s2(@ @c@ir)
                                                                                           and imaging treatment were equal. The means ofthe test-statistic
                                                                                           distributions                     are denoted                    E(X(f)Isp)                  and E(X(f)Isa),            and the
              was
      where @2 the residual mean square from the ANOVA and r was                           variances are denoted by var(X(f)Isp) and var(X(f)Isa). The
      the number of human observers. Furthermore, the bounds on the                        numerator and denominator in equation 9 are measures of the
      95% confidence interval were calculated from                                         square of the signal and of the noise, respectively. For a sine
@
—                                               [r/(c   1)](i@ L)2                       lesion location and additive Gaussian noise, the NPW SNR is
                     F(cl)(cIXrI)         _                            ,           Eq.6    Given that the noise in the liver of the SPECT images was a good
                                                                                           approximation of additive Gaussian noise, that three different
                                                                                           tumor locations were rated by the human observers in a random
                                                                                           order and that the location to be evaluated was specified, the signal
@     where was the difference between a pair of SNRs. Equation 6                          and the noise were first calculated for each location and then were
      was solved for L, and the lower and upper bounds were equal to the                   averaged over location. The average signal was divided by the
      minimum and maximum roots, respectively. A statistically signifi                     average noise for each treatment to calculate an NPW SNR (25).
      cant difference between treatments at the 5% level required a test                          Using the average human SNR, the statistical efficiency of the
      statistic greater than F4,24= 2.78 and 95% confidence intervals that                 human observer with respect to the NPW observer was calculated
      did not include zero. The calculations required for two-way                          for each treatment with the ratio:
                         test
      ANOVA, Scheffé's and the bounds on the confidence interval
      were obtained from Pollard (37).                                                                                                                                    I
                                                                                                                                                                              /@@p@2humani
                                                                                                                                               Efficiency = ttSNR2Npw)@                                                   Eq. 10

      Comparison of Human and Non-Prewhitenlng
      Observers                                                                            For many tasks, this efficiency has been in the range of about 0.5 ±
                                                                                           0.2, when the displayed contrast was sufficient for the specified task
        An imaging system can be mathematically described by
                                                                                           (21).
                                      g = Hf + n,                                  Eq. 7          The relation between                                      the SNRs of the human and NPW



                                                                               SCATFER SUBTRACTION IN HEPATIC SPECT                                                                d
                                                                                                                                                                                 • e Vries et a!.                       1015
    observers was examined using nonparametric correlation analysis          which is equal to the sum of the mean square bias and the variance.
    for two reasons: (a) Knowledge of the probability distribution           Finally, the squared SNR of the ROI estimator was defined as the
    functions from which the SNRs were drawn was unavailable; and            reciprocal of the EMSE normalized by the square of the object
    (b) with a relatively small number of SNRs to be examined, the           strength (23):
    assumption of normal distributions for the SNRs was questionable.
    By assigning integer ranks to the SNRs, a correlation between                                                                  E(O2)@                                       16
                                                                                                                                                                               @.
                                                                                                             cx@i@2 _ _______________
@                                                                                                                ROl
    SNRs was examined using the linear correlation coefficient of the                                                          EMSE(OROI)
    ranks. Spearman's rank correlation coefficient, Ps was used, with a
    null hypothesis of no correlation between the human and NPW                The estimation of activity in ROIs was performed using the
                      =
    SNRs (i.e., H@:p5 0). The alternative hypothesis, HA, was that           tumor-present images ofthe ROC experiments before the interpola
    there was a direct correlation of human SNRs with NPW SNRs               tion and scaling to gray-level values for display. For both cold and
    (i.e., a tendency for large human and NPW SNR values to be                                                           value
                                                                             hot tumors, the calculation of the “true― of activity, 0, was
    paired), so a one-tailed test of the significance of Ps was performed.   done using the noise-free primary SPECT image for each tumor
                                                                             location. These images were corrected for attenuation but did not
    Comparison of Detection and Quantitation                                 havethe Butterworth   low-passfilteringthat was appliedto the
      Activity quantitation is an example of a task where the strength       noisy images.
    (or magnitude) of a parameter, 0 (e.g., the number of counts in a           With the noise-free primary SPECT image of the tumor as the
    region), is desired. The strength of the parameter in a region of an     standard for the EMSE calculations, activity estimates from the
    object, f, may be defined as the sum of the elements that are            prim@y images were affected only by noise. Therefore, the ROI
               w
    contained ithina region   defined                w.
                                      bya template, Withtheobject            sr'u@fortheprimary    images  wasbydefinition               T
                                                                                                                             thebestcase. hisis
    and the template represented as arrays of N elements, the true value     similar in concept to the detection experiments, where the primary
    of 0 is given by:                                                        image was defined as the ideal scatter subtraction.
                                         N                                      The       ROl    SNR    of   the   activity      estimates    was    calculated       for   each
@                                  0=             w1f@.             Eq. 11           andthenwascompared iththedetection
                                                                             treatment                w               SNRsfromthe
                                        1=I                                  human        and    NPW       observers.         Spearman's      rank    correlation       coeffi
                                                                             cient was used to test for correlation                   between    SNRs of the detection
    When ROI estimation is used to measure activity in an estimate of
    the object (i.e., an image), the same template is applied directly to                tasks. henullhypothesis,
                                                                             andestimation    T                H0,wasthatPs 0; the
    theestimate   (23),1,whichwasareconstructed    SPECTimage      inour     alternative hypothesis, 11A'was that there was a direct correlation
    experiments. The ROl estimate of 0 is given by:                          of the estimation SNR values with the detection SNR values.
                                              N
@                              0ROi           @:                    E@. 12   RESULTS
                                          i=1
                                                                             Human Observer Detection Accuracy
       In contrast to the NPW template, which had the profile of the           The average ROC curves for each treatment are shown in
    lesion, the template for the ROl estimator was a circular disk,
    having the diameter of the lesion and pixel values of either one or      Figure 2, for the cold and hot tumor experiments, respec
    zero for pixels located entirely inside or outside of the ROI,           tively. For both lesion contrasts, comparison of the curves
    respectively. If a fraction of a pixel was included in the ROl,          from primary images with curves from uncorrected images
    subsampling of the edge pixels of the disk provided pixel values         of both low- and high-scatter conditions showed an obvious
    between zero and one. Thus, the ROI estimator simply summed the          decrease in detection accuracy (i.e., the AUC or SNR) as the
    counts detected within the ROI.                                          amount of scatter increased. The effect of DPW scatter
       Barrett (23) recommended the use of the ensemble mean square          correction on detection was not as clear.
    error (EMSE) as a figure of merit for the ROI estimator to account          The results of the two-way ANOVA of the SNRs gave
    for both bias and variance. Using notation similar to Barrett's, the     strong evidence for the existence of real, statistically signifi
    bias of the estimator was given by the difference between the            cant differences              between        treatments.         As shown            in Table 2,
    averaged estimates and the true value of 0:                              the calculated F statistics were 13.45 (P = 0.7 X 10@) and
                          bRo! E(ORoI)fl!f      @,                  Eq. 13   20.26 (P = 0.2 x 106) for cold and hot tumors, respec
                                                                                                 =
                                                                             lively. With F4@24 2.78 for a = 0.05, the null hypothesis
                  is the
    where E(O)@j@ estimate of activity in the ROI averaged over n            that the differences between average SNRs of the treatments
    noise realizations for a particular object, f (i.e., a lesion at a       were equal to zero was rejected for both contrast polarities.
    particular location). The mean square bias was defined as the               The results            of applying            Scheffd's       multiple       comparisons
                                                   The
    squared bias averaged over all objects: E(b@01)@. variance of the
    estimator was given by                                                   test for paired samples to the differences in the average
                                                                             human SNR between selected pairs of treatments are
                      var(ORoI)       E([OR0I        °ROI])n.f,    Eq. 14   presented          in Table 3 and in Figure 3 for cold and hot tumors,
                                                                             respectively. The primary images gave a statistically signifi
    where the average ofthe squared differences between estimates and        cant (P < 0.05) increase in detection accuracy over the
                       is                                a
    themeanestimate takenoverall noiserealizations ndoverall
                                                                             uncorrected low-scatter images (A versus B) only for hot
    lesion locations. The EMSE was then defined as the average
    squared difference of the estimates and the true parameter value, 0:
                                                                             lesions. Although the ROC curves for the cold lesions appear
                                                                             to have a real difference, the null hypothesis (i.e., the
                      EMSE(OROI)         E([ORol          0]2)@f,   E@. 15   difference         is equal      to zero)        could     not   be rejected.          However,




    1016       Tm@      O        MEDICINE Vol. 40 • 6 •
                  JOURNAL FNUCLEAR      •         No.   June 1999
    A                ROC
                       Curves Le&onsB
                            C
                 Averoqe for old

@ :: C
     0
     U
     0
     L@.
       0.6           ///
                                                                          U
                                                                          0
                                                                           C
                                                                           0


                                                                          L'.
                                                                                                                                        FIGURE2. Fitted,averagereceiveroper
                                                                                                                                        ating characteristic(ROC) curves from
                                                                                                                                        seven independent human observers for
                                                                                                                                        experiments    that included primary images,
                                                                                                                                        uncorrected images for low- and high-scatter
                                                                                                                                        conditionsand dual photopeakwindow (DPW)
     a
                 f/.
                 @l               Treatment              AUC SNR
                                                                          a
                                                                                                   Treotrnent           AUC SNR         correctedimagesfor low- and high-scatter
                                                                                                                        .84 1.40
     a. 0.4 r,@ — k Primory                            .88 1.67
@    0                                                                    0            A@i            Primary                           conditions. Curves are shown for images with
                                                                          a.
                /i         ...    B: Uncorr, Low Scot    .86 1.51         a           ,;‘i . . - B: Uncorr, LowScot   .80 1.19        cold Ieskxis (A) and images with hot lesions
                !                  U High Scot
                                  C: ncorr, .811.24
     I-                                                                         0.2       DPW, .81 .92
                                                                                      P .._.. .74 1.25
                                                                                                   C:
                                                                                       @,, —— Uncorr, High Scot

                                                                                         E:Low
                                                                                         D:High 1.07
                                                                                             Scot
                                                                                          DPW,
                                                                                        —.-- .78
                                                                                             Scot
                                                                                                                                        (B). Taskwas detection 2.5-cm-diameter
                                                                                                                                                                  of

@
          0.2

                  -       -
                           —...- .83
                                Scat
                             DPW,
                            E:High 1.33
                           _•_@_
                              D'.DPW,LowScot .85 1.48

          0.1' • . - - ‘ I - - - !                                          nfl
                                                                                                                                                   h
                                                                                                                                        tumor; whk@had contrast of 13% (-13% cdd
                                                                                                                                        and +13% hot) and was located at one of
                                                                                                                                        three possiblesites.AUG and corresponding
           0.0 0.2 0.4 0.6 0.8                                  1.0               0.0       0.2       0.4      0.6      0.8       1.0 SNA are reported. (For clarity,error bars were
                                      P      Fraction
                                  Folse o&tive                                                    FolsePositiveFraction
                                                                                                                                        omitted.)


    for both contrast polarities, primary images gave a signifi                                             Comparison of Human and Non-Prewhitening
    cant (P < 0.05) increase in detection accuracy in compari                                               Observers
    son to uncorrected                    high-scatter      images       (A versus          C), and            The average human SNR, the NPW SNR and the human
    uncorrected low-scatter images gave significantly greater                                               efficiency are reported for each treatment and contrast
    (P < 0.05) detection accuracy than uncorrected high-scatter                                             polarity in Table 4. Both the human and NPW observers
    images (B versus C).                                                                                    produced lower SNRs for the hot lesions in comparison to
      Visual inspection of the ROC curves for the comparison                                                the cold lesions.
    of DPW scatter correction with uncorrected low-scatter                                                     A positive correlation between the human and NPW
    images            (D versus          B) showed        little difference             in detection        observers is evident in Figure 4, with an apparent               separation
    accuracy.               For the high-scatter             condition,         curves for the              Of the points associated with the DPW-processed                  images (D
    comparison  of DPW-corrected images versus uncorrected
                                                                                                            and E) from those of uncorrected images (B and C). Linear
    images (E versus C) showed more noticeable separation as
                                                                                                            fits to the primary         and DPW-corrected         data (slope         0.41,
    the difference                   in the SNRs (derived                 from the AUCs)
                                                                                                            intercept = 0.42) and to the primary and uncorrected data
    gradually               increased.        However,      given     the variances           of the
                                                                                                            (slope = 0.7 1, intercept           = —0.40), which      are      shown       in
    curve fits and resulting AUCs, as well as the sacrifice of
                                                                                                            Figure 4, further emphasize the apparent difference in the
    power with the conservative approach to reducing type I
                                                                                                            way the human and NPW observers responded to the
    errors       inherent           in Scheffé's multiple           comparisons            test, the
    difference in SNRs for any comparison of DPW scatter                                                    DPW-corrected          images.
    correction with uncorrected images was too small to demon                                                   With cold and hot tumor SNRs pooled, Spearman's rank
    strate statistical significance (i.e., the null hypothesis could                                        correlation       coefficient    gave a strong and significant        correla
    not be rejected).                                                                                       tion betweenthe ranks of human and NPW observerSNRs
       For the comparison of primary images with DPW                                                        associated        with the primary     and non-DPW       treatments       (A, B
    corrected low-scatter images (A versus D), the null hypoth                                              and C) and the primary and DPW treatments (A, D and E).
    esis could not be rejected.                    However,         detection         accuracy    was       The correlation remained significant but decreased when all
    significantly greater for primary versus the DPW-corrected                                              treatments        were considered      together.   Therefore,    correlation
    high-scatter                 images (A versus E).                                                       between the human and NPW SNRs was demonstrated,


                                                                                                   TABLE 2
                                                                Two-Way ANOVA ofAverage Human Observer SNR

                                                lesionsSum                            lesionsHot
                ofMeanvariationsquaresdfsquare
                Source ofCold         ofMeanSum
          FPsquaresdfsquareFPBetween
          3.940.0070.2560.0413.720.009Between
                  observers0.3560.058
          106Residual0.35240.0150.26240.011Total1.49341.4134ANOVA
                  treatments0.7940.197                     13.450.7                                           x iO@0.9040.22520.260.2                                             x




                                    o          SNA = signal-to-noise
                           = analysis fvariance;                   ratio; df =degree of freedom.



                                                                                         SCArIER       SUBTRACTION            IN HEPATIC SPECT            de Vries
                                                                                                                                                        •            et al.         1017
                                                              TABLE 3
                                            P
                                   Scheffé's airwise Multiple Comparisons Testfor ROC Results*

                      lesionsDifference    GoldlesionsHot
   ConfidenceComparison    of                Test95%          ConfidenceDifference                    ofTest95%
                   meanSNAs
   SNAsstatistictintervalAversus           statistictintervalmean
            B
    0.39Aversus           0.16                1.61—0.05,                0.380.203.200.01                                           ,
    0.33D D               0.19                2.16—0.03,                0.410.151.71—0.04,
      versusB
    0.24B                —0.03              0.04—0.24,                0.190.050.23—0.13,
      versusC
    0.46Aversus           0.27                4.310.05,                   0.480.275.810.08,
            C
    0.66Aversus            0.43              11.190.22,                   0.650.4717.640.29,
    0.51E      E            0.34              7.020.13,                   0.560.328.300.14,
       versus 0.34differences
               C            0.09              0.48—0.13,                0.310.151                               .74—0.04,

  0.05).tCritical                 (P
                     aresignificant <
  0.05.ROC          =
          value:F4,24 2.78,P <
                                        S                   ratio.
       = receiveroperatingcharacteristic; NR= signal-to-noise


andthenullhypothesisthatp,=OwasrejectedwithP<                               hypothesis was rejected at the P < 0.05 level only when the
0.05. The results are reported in Table 5. The P values were from           SNRs of the non-DPW treatments (i.e., A, B, and C) were
the one-sided test with HAspecifying direct correlation.                    considered. The results are reported in Table 5. The P values
                                                                            were from the one-sided test with HA specifying direct
                                                                            correlation.
Comparison of Detection and Quantitation
   The results of activity quantitation using the ROl estima
tor are summarized for both cold and hot tumors in Table 6                  DISCUSSION
and Figure 5. Note that the magnitude of the EMSE is                           The ROC experiments          indicated that human detection
inversely proportional to the SNR for the ROI estimator.                    accuracy       in SPECT    images   decreased   as the amount        of
The bias and variance for the primary images (A) were                       scatter present increased. For both contrast polarities, uncor
affected only by the random       noise due to counting     statistics,     rected low-scatter images gave significantly higher detection
given that the noise-free primary image corrected for                       accuracy than the uncorrected high-scatter images. Further
attenuation was used as the standard against which all                      more, although the higher detection accuracy was statisti
activity estimates were compared. Bias increased as the                     cally significant only for hot lesions when primary images
amount of scatter in the uncorrected images increased from                  were compared with uncorrected              (
                                                                                                                   @mTci.e., low scatter)
low (B) to high (C), with a decrease in variance as the                     images, the increase in accuracy was significant for both hot
number    of counts   in the images       increased.      The   DPW         and cold lesions when primary         images were compared      with
corrected images for both low and high scatter (D and E,                    uncorrected high-scatter images.
respectively) showed the decreased bias obtained by scatter                    However, the subtraction of estimated scatter by means of
subtraction, with the cost of increased variance due to a                   the DPW method failed to demonstrate statistically signifi
reduction in the counts in the projection image set and an                  cant improvement in detection accuracy over uncorrected
alteration of the noise characteristics      of the reconstructed           images. Moreover, for the high-scatter images of both
    images.
SPECT                                                                       contrast polarities, primary images gave significantly better
   The SNR of the ROI estimator reported in Table 6 is                      detection accuracy than the DPW-corrected images. Whereas
shown in Figure 6, which provides a visual comparison with                  the primary and DPW-corrected images had count levels
the average human SNR and the NPW SNR. Like the                             that were lower than the levels in the uncorrected
detection SNRs, the ROI estimator SNR was greatest for the                  images, the DPW-corrected images generally exhibited
primary images and decreased as the amount of scatter in the                more prominent correlated noise blobs than either the
images increased. Unlike the detection SNRs, a notable                      primary or the uncorrected images for both low- and
increase in the ROl SNR was produced by the DPW scatter                     high-scatter cases.
subtraction.                                                                   The noise characteristics of the DPW images may have
   With cold and hot tumor SNRs pooled, the comparison of                   differed from those of the other treatments due to overcorrec
the average human SNR with the ROI SNR using Spear                          tion of the projection sets (as seen in Table 1) and to the
man's rank correlation coefficient resulted in rejection of the             subtraction of smoothed estimates of scatter from the
null hypothesis (i.e., p. = 0) at the P < 0.05 level only when              projections, as opposed to the rejection of the true scatter
SNRs from all treatments were considered together. For the                  before image acquisition.      It is known that noise correlations
comparison     of the NPW SNR with the ROI SNR, the null                    have an adverse effect on the ability of the human observer




1018         Tm@                MEDICINE Vol. 40 • 6 •
                Joui@mi OFNUCLEAR      •         No.   June 1999
@                                                      +




                                                                             to detect lesions in a background (26). The liver presented a
     A                                                                       large, fairly uniform, region of activity in the SPECT
             1.0
                                                                             images, in which noise blobs provided the primary source of
                                                    P<0.05                   distraction for the observers.
     z                                                 I     P<0.05
     U)                                                                         Both the human and the NPW observers indicated that
     C                                     P<O.05
             0.5                                                             detection accuracy was somewhat lower for hot lesions in
     a,
     U
     C                                                                       comparison    to cold lesions. However,    the difference   in
     a,
     I-
     a,                                                                      magnitude    did not affect the conclusion    that increased
     0                                                                       scatter in the SPECT images decreased the detection SNR.
     C
             0.c
     0                                                                       Nor did the difference affect the fact that the DPW scatter
     a,
                                                                             subtraction produced inconclusive results with respect to
                                                                             detection.
           _n c                                                                 The correlation of the NPW and human SNRs indicated
                       A—B A—D D—B B—C A—C A—E E—C             that the NPW observer can be a useful predictor of how
                                  Trsotrv*n(s Comporsd
                                                                             human observer detection accuracy is affected by scatter in
     B                                                                       SPECT     undercertainconditions.
                                                                                  images                     Therewasa strong,
             1.0
                                                                             direct correlation between human and NPW observer SNRs
                                                    P<0.05                   when uncorrected results and DPW-corrected results were
     z                                                                       considered separately. However, the NPW observer ap
     U,
     C       0.5                           P<O.05                            peared to be somewhat less effective for predicting the
                   P<0.05
     a,
     U
     C
                                                                             human observers' performance when DPW-corrected and
     a,
                                                                             uncorrected          images    were considered        together.   The DPW
     a,

     0
     C
             0.0                  +
                        4 + 4 1 +@T                                          correction generally caused an increase in the human SNR
                                                                             with respect to the uncorrected images, while the NPW SNR
                                                                             decreased.
                                                                                The discrepancies between the two types of observers
                                                                             may indicate that they responded differently to the effect of
                       A—B A-.D     D—B B—C A—C A—E E—C          the DPW correction on noise correlations. It is possible that
                                     Treetmant. Cornpor.d
                                                                             human observers were able to do some decorrelation of
                                                                             image noise with partial prewhitening (38). Perhaps a model
    FiGURE 3.       Comparisons of human observer signal-to-noise            observer      that     included       the effects   of spatial    frequency
    ratios (SNR5) from ROC experiments for selected pairs of          selective channels in the human visual system would
    treatments are presented for cold (A) and hot lesions (B).        provide an improved prediction of human performance
                          c
    Between-treatment omparisons        were made using Scheffé's
                                                                      (24,26).
    methodof multiplecomparisonsof pairedsamples(test statistics
    are reported in Table 3). Mean difference in detection SNAs,         As expected, for the task of estimating activity, the
    averaged over seven observers, was plotted for each compan        results showed that quantitative accuracy decreased as
    son. Bars indicate 95% confidence intervals. Nullhypothesis was the amount of scatter present increased. In addition, the
    that mean difference was equal to zero. Statistically significant SNR of the ROI estimator indicated that scatter sub
    differences are labeled with P < 0.05.
                                                                      traction improved the accuracy of quantitative measure
                                                                      ments on average. Although the ROC experiments did not
                                                                      demonstrate a significant improvement in detection accu

                                                                        TABLE4
                                    Average Human Observer SNR, NPW Observer SNA and Human Efficiency

                               lesionsAverage         Cold lesionsHot
                                humanNPWHumanAverage
           humanNPWHumanTreatmentSNA
               (SD)SNRefficiencyA1(SE)SNRefficiencySNA
               (0.02)2.610.28B1.51 (0.04)2.970.311
                                 .67                                                               .40
               (0.02)2.260.28CI      (0.02)2.450.381.19
               .980.22D1             .23 (0.02)2.290.290.92                                              (0.01)1
               .980.40E1             .48 (0.02)2.390.381                                           .25(0.01)1
          .810.35SNA                 .33 (0.01)2.020.431                                           .07 (0.03)1


              = signal-tonoise     N
                              ratio; PW= non-prewhitening.




                                                                  SCATFER SUBTRACTION IN HEPATIC SPECT                       d
                                                                                                                           • e Vries et al.        1019
                                                                3
                                                                                   Contrast
                                                                        TreatmentLe&on
                                                                             HotA Cold

                                                                2               B             •       G                                     I
                                                                                                                                                      I

                                                         z                      C             A         i@
                                                                                                                                         I
                                                                                                                                         @... . ...
                                                         (I)
                                                         C                      D             •       0
    FIGURE4. Forbothcoldandhotlesions,
                                                         0
                                                         E
                                                                                EU            •0      0             ...@tr1
    scatter plot of average human observer
    signal-to-noise   ratio (SNR) versus       non       I      1
                                                                                                       ,...;@k4'
    prewhitening (NPW) quasi-ideal observer
    SNR showscorrelation   betweendetection
    accuracy of two types of observers. Differ                                                                         Uneor fits to:
    ences     in dashed   and dotted    lines fit to                                                                         A, B, and                     C
    primary and uncorrecteddata (A, B and C)                                                                                 A,D,ondE
    and to primaryand DPW-correcteddata (A,
    D and E), respectively, suggested that hu                   0                                              I

    man and NPW observers may respond                               0                                       2                        3                              4
    differently to effects of DPW method         on                                                      NPW SNR
    image noise.


    racy with DPW scatter subtraction, DPW substantially                           strength of the correlation between the SNRs for the two
    decreased the bias at the cost of increased noise, as                          tasks.
    evidenced by the increased variance. Furthermore, where                           Before generalizing the results of the ROC experiments,
    as the ROl SNR for DPW-corrected images was better                             several considerations regarding the conditions under which
    than that of uncorrected images (comparing treatments D                        they were conducted should be considered. First, for the
    to B for low scatter and E to C for high scatter), it was                      clinical application considered, the attenuating medium was
    always lower than the ROI SNR of primary images (treat                         nearly uniform, unlike locations such as the thorax and
    ment A).                                                                       certain regions of the head. Second, the experiments tested
                               wasseenbetweenthe human
       A strongdirectcorrelation                                                   only the simple detection task under SKE conditions. This
    and NPW detection SNRs, but the correlation of the ROI                         required       the use of images with low contrast             and low counts
    estimator SNRs with both detection SNRs (i.e., human and                       (i.e., high noise) to obtain suitable areas under the ROC
    NPW) was weaker. Barrett (23) gave the relationship                            curves. Other tasks that are part of clinical decision making
    between    the NPW SNR and the ROI SNR as                                      were not considered, such as the ability to correctly locate or
                              CKTD 2
                               @3F@
                                                                                   to correctly determine the size of a lesion. Third, filtered
                                                                        Eq.l7      backprojection was used to reconstruct the images, which
@                              SNR@0J                                              produces particular artifacts and noise characteristics that
    where Q is a product of factors, which accounts for the                        differ from other algorithms, such as the iterative methods.
    different effects that characteristics of images (e.g., bias and               Fourth,    observers      were not allowed     to adjust                the transfer
    correlated noise) have on the detection and estimation tasks.                  function of the display monitor to their liking. The display
    Some of these factors may explain the difference in the                        monitor was carefully controlled throughout all of the


                                                                           TABLE5
                      Spearman's      Rank Correlation       Coefficient for Comparisons           of Detection and Estimation    SNR5*

                                                             Sample                   SNRversus                      SNR versus                    SNA versus
       SNAPrimary Treatments                                   sizeHuman         NPW SNAHuman                      AOl SNRNPW                     AOl

       0.04)Primaryuncorrected (A, B and C)
               and                                              60.94                (P = 0.002)0.66                (P = 0.08)0.77                        (P =
       0.08)Alland DPWcorrected (A,D and E)                     60.94                (P = 0.002)0.49                (P = 0.16)0.66                        (P =
       0.14)*@ldface (A,B, C, D and E)
          treatments                                           100.81                (P = 0.002)0.60                (P = 0.03)0.38                        (P =


       0.05).SNA correlationcoefficients            (P
                                        aresignificant <
            = signal-to-noise ratio; NPW = non-prewhitening;AOl=            region of interest.




    1020                   OFNUCLEAR
                THEJout@i'@i              •         No.   June 1999
                                   MEDICINE Vol. 40 • 6 •
                                                                                              TABLE 6
                            Region-of-lnterest             (ROl) Estimation            ofActivity Using the Ensemble      Mean Square    Error (EMSE)

                     87.3)Mean Coldlesions (counts in AOl =74.1)Hot                                                          lesions (countsin AOl =
                  estimatedMean-squareMean
    Mean-squareTreatmentcountsbiasVarianceEMSEAOl                     estimated
                                                           SNRcountsbiasVarianceEMSEAOl
     SNRA73.90.64.75.332.386.90.45.25.637.0B71.911.23.614.819.381.342.73.245.912.9C87.3200.62.9203.55.295.188.32.490.75.2D74.70.8




               = signal-to-noise
                               ratio.



    experiments         to maintain              a consistent             log-linear     transfer       observer performance; the ROl estimator was less effective
    function     and thus to minimize                    effects of the display           on the        in predicting detection accuracy. The results suggest that to
    outcome of the experiments. Fifth, pooling the results from                                         achieve improved accuracy for both detection and quantita
    the several lesion locations had an averaging effect that                                           tion either scatter correction algorithms must produce results
    obscured the differences in detection and estimation SNRs                                           that approach the ideal conditions of primary images or
    that can arise due to location (39). Finally, statistically                                         detectors must have improved energy resolution for scatter
    significant differences are not necessarily equivalent to                                           rejection.
    clinically significant differences.

    CONCLUSION                                                                                          ACKNOWLEDGMENTS
           For both hot and cold tumors in the liver, primary images                                       This study was supported by the National Cancer Institute
    produced        detection       and quantitation                SNRs that were supe                 under grant CA-42l65. Its contents are solely the responsi
    nor to the other treatments. The greatest improvement was                                           bility of the authors and do not necessarily represent
    seen in the cases where the scatter fraction was high. Scatter                                      the official views of the National Cancer Institute. We
    subtraction with the DPW method produced an increase in                                             thank Drs. Stephen C. Moore and Harrison H. Barrett for
    quantitative accuracy that was greater than the increase in                                         helpful conversations and advice regarding the design
    detection accuracy. The NPW observer model was fairly                                               and implementation of the experiments discussed in this
    effective at predicting the trends of the average human                                             article.



                              ROl Est@mat@onof Counts                                            Lesons
                                                                                                @n
@             120                       I         I        I         -1       1
                        -   —   @‘True―   Counts         in   ROl


                    0 Meon Estimoted Counts in ROl
              100 - •IMeon Biosl (scaled by 5.0)
                                                                                                          T
               80           •1@                              -T- -
      (I)
     4-,
      C
@              60
      0
     0
               40                                                                                                           FIGURE 5. Regionof interest(ROI) esti
                                                                                                                            mator activity estimates are plotted (light
                                                                                                                            bars) with variance indicated by error bars
               20                                                                                                           (+1 SD). Absolute value of bias (dark bars)
                                                                                                                            is also shown. Notedifferentvertical scales.
                                                                                                                                                        activity in ROl,
                                                                                                                            Dashed lines indicate “true―
@                      _
                 0 _ . —                                                  .
                                                                    . L._11_@ .                     .      . —
                                                                                                               .            ascalculated fromnoise-free primary  image
                 Cold:       A         B         C        D          E Hot: A               B       C       D    E          corrected for attenuation. Results for both
                                                                      Treatment                                             cold and hot lesions are shown for each
                                                                                                                            treatment.




                                                                                   SCATI'ER SUBTRACTION IN HEPATIC SPECT                    d
                                                                                                                                          • e Vries et al.      1021
                                                                                         Le&on Detection & EstimaUon SNRs
                                                                                      BARS: DNPW                     SNR                          SYMBOLS: Human
                                                                                                      Estimator
                                                                                                  U ROl     SNR                                            SNR
                                                                                                           (scaled by 0.1)




                                                                       z
                                                                      U)


FIGURE6. For both cold and hot lesions,
averagehumanobserver   signal-to-noisera
tio (SNR) (symbols), non-prewhitening
(NPW) observer SNR (light gray bars) and
                    e        S
regionofinterest(ROl) stimator NR(dark
gray bars) are shownfor each treatment.
The symbolsused to show human SNR                                             Cold: A             B        C         D         E Hot: A              B       C       D       E
correspond to those in correlation plot in                                                                                      Treatment
Figure4.


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