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Speckle Correlation Analysis

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					Adaptive Imaging Preliminary:
 Speckle Correlation Analysis
            Speckle Formation
• Speckle results from coherent interference of un-
  resolvable objects. It depends on both the
  frequency and the distance.




                                     sample
     transducer                      volume
 Speckle Second-Order Statistics
• The auto-covariance function of the
  received phase-sensitive signals (i.e., before
  envelope detection) is simply the
  convolution of the system’s point spread
  function if the insonified region is
   – macroscopically slow-varying.
   – microscopically un-correlated.
 Speckle Second-Order Statistics

• The shape of a speckle spot (assuming fully
  developed) is simply determined by the
  shape of the point spread function.
• The higher the spatial resolution, the finer
  the speckle pattern, and vice versa.
           Speckle Statistics
• The above statements do not hold if the
  object has structures compared to or larger
  than the ultrasonic wavelength.
• Rician distribution is often used for more
  general scatterer distribution.
• Rayleigh distribution is a special case of
  Rician distribution.
      van Cittert-Zernike Theorem
• A theorem originally developed in statistical
  optics.
• It describes the second-order statistics of the field
  produced by an in-coherent source.
• The insonification of diffuse scatterers is
  assumed in-coherent.
• It is different from the aforementioned lateral
  displacement.
   van Cittert-Zernike Theorem
• The theorem describes the spatial
  covariance of signals received at two
  different points in space.
• For a point target, the correlation of the two
  signals should simply be 1.
• For speckle, correlation decreases since the
  received signal changes.
   van Cittert-Zernike Theorem

• The theorem assumes that the target is
  microscopically un-correlated.
• The spatial covariance function is the
  Fourier transform of the radiation pattern at
  the point of interest.
    van Cittert-Zernike Theorem




radiation pattern      correlation
   van Cittert-Zernike Theorem
• The theorem states that the correlation
  coefficient decreases from 1 to 0 as the
  distance increases from 0 to full aperture
  size.
• The correlation is independent of the
  frequency, aperture size, …etc.
   van Cittert-Zernike Theorem
• In the presence of tissue inhomogeneities,
  the covariance function is narrower since
  the radiation pattern is wider.
• The decrease in correlation results in lower
  accuracy in estimation if signals from
  different channels are used.
van Cittert-Zernike Theorem

     correlation




                   distance
          van Cittert-Zernike Theorem



                     RF Signals
Channel




                                  Time (Range)
 van Cittert-Zernike Theorem
(Focal length 60mm vs. 90mm)
 van Cittert-Zernike Theorem
(16 Elements vs. 31 Elements)
van Cittert-Zernike Theorem
   (2.5MHz vs. 3.5MHz)
van Cittert-Zernike Theorem
     (with Aberrations)
   Lateral Speckle Correlation



correlation coefficient




                          displacement
                L/2
    Lateral Speckle Correlation
• Assuming the target is at focus, the
  correlation roughly decreases linearly as the
  lateral displacement increases.
• The correlation becomes zero when the
  displacement is about half the aperture size.
• Correlation may decrease in the presence of
  non-ideal beam formation.
Lateral Speckle Correlation
         14.4 mm Array
Lateral Speckle Correlation
Lateral Speckle Correlation
Lateral Speckle Correlation
    Lateral Speckle Correlation:
Implications on Spatial Compounding
           Speckle Tracking
• Estimation of displacement is essential in
  many imaging areas such as Doppler
  imaging and elasticity imaging.
• Speckle targets, which generally are not as
  ideal as points targets, must be used in
  many clinical situations.
           Speckle Tracking
• From previous analysis on speckle analysis,
  we found the local speckle patterns simply
  translate assuming the displacement is small.
• Therefore, speckle patterns obtained at two
  instances are highly correlated and can be
  used to estimate 2D displacements.
           Speckle Tracking
• Displacements can also be found using
  phase changes (similar to the conventional
  Doppler technique).
• Alternatively, displacements in space can be
  estimated by using the linear phase shifts in
  the spatial frequency domain.
           Speckle Tracking
• Tracking of the speckle pattern can be used
  for 2D blood flow imaging. Conventional
  Doppler imaging can only track axial
  motion.
• Techniques using phase information are still
  inherently limited by the nature of Doppler
  shifts.
Adaptive Imaging Methods:
Correlation-Based Approach
  Sound Velocity Inhomogeneities

                   body wall   viscera




                                         point of interest


                    v1 v2 v3
transducer array
Sound Velocity Inhomogeneities

                 Velocity (m/sec)
       water            1484
       blood            1550
    myocardium          1550
         fat            1450
        liver           1570
       kidney           1560
Sound Velocity Inhomogeneities
• Sound velocity variations result in arrival
  time errors.
• Most imaging systems assume a constant
  sound velocity. Therefore, sound velocity
  variations produce beam formation errors.
• The beam formation errors are body type
  dependent.
Sound Velocity Inhomogeneities


       no errors         with errors
• Due to beam formation errors, mainlobe
  may be wider and sidelobes may be higher.
• Both spatial and contrast resolution are
  affected.
       Near Field Assumption
                              beam formation
    geometric delay
                                                        aligned




                 velocity
                                           correction
                 variations
• Assuming the effects of sound velocity
  inhomogeneities can be modeled as a phase
  screen at the face of the transducer, beam
  formation errors can be reduced by
  correcting the delays between channels.
Correlation-Based Aberration Correction
                No Focusing
Correlation-Based Aberration Correction
              Transmit Focusing Only
Correlation-Based Aberration Correction
           Transmit and Receive Focusing
Correlation-Based Aberration Correction

    Wire: Before Correction   Wire: After Correction
Correlation-Based Aberration Correction

   Diffuse Scatterers: Before   Diffuse Scatterers: After
    Correlation Based Method
                    1 T
           Cn (t )   S n ( ) S n 1 (t   )d
                    T 0

                  tn  max Cn (tn )
                           t n


• Time delay (phase) errors are found by
  finding the peak of the cross correlation
  function.
• It is applicable to both point and diffuse
  targets.
    Correlation Based Method
                       n
             Tn     t
                      i 1
                             i




• The relative time delays between adjacent
  channels need to be un-wrapped.
• Estimation errors may propagate.
     Correlation Based Method

                  filter   correlator


                             x


• Two assumptions for diffuse scatterers:
  – spatial white noise.
  – high correlation (van Cittert-Zernike theorem).
     Correlation Based Method


• Correlation using signals from diffuse
  scatterers under-estimates the phase errors.
• The larger the phase errors, the more severe
  the underestimation.
• Iteration is necessary (a stable process).
         Alternative Methods

• Correlation based method is equivalent to
  minimizing the l2 norm. Some alternative
  methods minimize the l1 norm.
• Correlation based method is equivalent to a
  maximum brightness technique.
                    Baseband Method

         1 T                            1 j0 tn T
Cn (t )   BBn ( ) BBn 1 (t   )d  e
                       *
                                                 0 A( ) A(t    tn )d
         T 0                            T
                             tan 1 (Im( Cn (0)) / Re( Cn (0)))
                    t n 
                                            0

    • The formulation is very similar to the
      correlation technique used in Color Doppler.
       Baseband Method
    Cn (0)                      *
                        BBn (m) BBn 1 (m)
               mregion of interest


I                                        acc.
            CORDIC
Q


    sign control      Q sign bit

I                                        acc.
            CORDIC
Q                                        acc.
     One-Dimensional Correction:
             Problems
• Sound velocity inhomogeneities are not
  restricted to the array direction. Therefore, two-
  dimensional correction is necessary in most
  cases.
• The near field model may not be correct in
  some cases.
One-Dimensional Correction:
        Problems
One-Dimensional Correction:
        Problems
  Two-Dimensional Correction
• Using 1D arrays, time delay errors can only
  be corrected along the array direction.
• The signal received by each channel of a 1D
  array is an average signal. Hence,
  estimation accuracy may be reduced if the
  elevational height is large.
• 2D correction is necessary.
  Two-Dimensional Correction
• Each array element has four adjacent
  elements.
• The correlation path between two array
  elements can be arbitrary.
• The phase error between any two elements
  should be independent of the correlation
  path.
        Full 2D Correction
(1,1)   corr   (1,2)   corr   (1,3)
corr




                corr




                               corr
(2,1)   corr   (2,2)   corr   (2,3)
corr




                corr




                               corr
(3,1)   corr   (3,2)   corr   (3,3)
       Row-Sum 2D Correction
       (1,1)   corr   (1,2)   corr   (1,3)
corr




       (2,1)   corr   (2,2)   corr   (2,3)
corr




       (3,1)   corr   (3,2)   corr   (3,3)
Correlation Based Method: Misc.
• Signals from each channel can be correlated
  to the beam sum.
• Limited human studies have shown its
  efficacy, but the performance is not
  consistent clinically.
• 2D arrays are required to improve the 3D
  resolution.
  Displaced Phase Screen Model
• Sound velocity inhomogeneities may be
  modeled as a phase screen at some distance
  from the transducer to account for the
  distributed velocity variations.
• The displaced phase screen not only
  produces time delay errors, it also distorts
  ultrasonic wavefronts.
   Displaced Phase Screen Model



                   phase screen

• Received signals need to be “back-propagated”
  to an “optimal” distance by using the angular
  spectrum method.
• The “optimal” distance is determined by using
  a similarity factor.
Displaced Phase Screen Model
                TSC + BP
Time-shift compensation with back-propagation
                TSC + BP
Time-shift compensation with back-propagation
                TSC + BP
Time-shift compensation with back-propagation
                TSC + BP
Time-shift compensation with back-propagation
Abdominal Wall Measurements
Abdominal Wall Measurements
Abdominal Wall Measurements
 Displaced Phase Screen Model

• After the signals are back-propagated,
  correlation technique is then used to find
  errors in arrival time.
• It is extremely computationally extensive,
  almost impossible to implement in real-time
  using current technologies.
        Wavefront Distortion

• Measurements on abdominal walls, breasts
  and chest walls have shown two-
  dimensional distortion.
• The distortion includes time delay errors
  and amplitude errors (resulting from
  wavefront distortion).
        Phase Conjugation


phase screen at face   displaced phase
   of transducer       screen


     phase                phase




               f                    f
Phase Conjugation
                Phase Conjugation
No aberration


    At 0 mm


   At 20 mm



   At 40 mm



  At 60 mm
          Phase Conjugation

• Simple time delays result in linear phase
  shift in the frequency domain.
• Displaced phase screens result in wavefront
  distortion, which can be characterized by
  non-linear phase shift in the frequency
  domain.
          Phase Conjugation

• Non-linear phase shift can be corrected by
  dividing the spectrum into sub-bands and
  correct for “time delays” individually.
• In the limit when each sub-band is
  infinitesimally small, it is essentially a
  phase conjugation technique.
End 4/13/2005
Some of the Recent Developments
Real-Time In Vivo Imaging[15]
Real-Time In Vivo Imaging
Real-Time In Vivo Imaging
Real-Time In Vivo Imaging
Real-Time In Vivo Imaging
Real-Time In Vivo Imaging




              Distribution of time delay corrections
Clinical Imaging Using 1-D Array [16]
Clinical Imaging Using 1-D Array




  Before Correction   After Correction
Clinical Imaging Using 1-D Array




  Before Correction   After Correction
Clinical Imaging Using 1-D Array




    Channel Data   Complex Scattering Structures
 Real Time Adaptive Imaging with
1.75D, High Frequency Arrays [17]




       1D and 2D Least Squares Estimation
Real Time Adaptive Imaging with
 1.75D, High Frequency Arrays




   Before Correction   After Correction
Real Time Adaptive Imaging with
 1.75D, High Frequency Arrays




   Before Correction   After Correction
 Real Time Adaptive Imaging with
  1.75D, High Frequency Arrays




Original    1 iteration   4 iterations
Real Time Adaptive Imaging with
 1.75D, High Frequency Arrays




        Original   Receive Only
2D Correction Using 1.75d Array On
  Breast Microcalcifications [18]
2D Correction Using 1.75d Array On
    Breast Microcalcifications
2D Correction Using 1.75d Array On
    Breast Microcalcifications




     (also with a 60% brightness improvement)
2D Correction Using 1.75d Array On
    Breast Microcalcifications
2D Correction Using 1.75d Array On
    Breast Microcalcifications




                      (a)   1D
                      (b)   1D with correction
                      (c)   1.75D
                      (d)   1.75D with correction
    Adaptive Imaging Methods:
    Aperture Domain Processing
Parallel Adaptive Receive Compensation Algorithm
       Single Transmit Imaging
• Fixed direction transmit, all direction receive
Measuring Source Profile
Removing Focusing Errors
         Focusing Errors




No Aberrations       With Aberrations
 Single Transmit Imaging




No Aberrations   With Aberrations
                PARCA




No Correction           With Correction
Simplifications:
1. DFT vs. Single Transmit Imaging
2. Weighting vs. Complex Computations
DFT vs. Single Transmit Imaging




 Single Transmit Imaging   DFT
Adaptive Weighting
Adaptive Weighting
    Frequency Domain Interpretation
          of the Aperture Data Coherent

Speckle


                                                  Incoherent

Aberrated



     *P.-C. Li and M.-L. Li, “Adaptive Imaging Using the Generalized Coherence Factor”,
     IEEE UFFC, Feb., 2003.
                Coherence Factor (CF)
     •    A quantitative measure of coherence of the
          received array signals.
                              energy in the low - frequency region
         General Definition :
                                          total energy
                         N 1          2

                          C (i, t )
                          i 0
                                               Coherent sum (DC)
              CF(t )      N 1

The larger, the better? N  C (i, t )
                                           2
                                               Total energy (times N)
                          i 0

             N: the number of array channels used in beam sum
             C(i,t) : the received signal of channel i
Determination of the Optimal
   Receive Aperture Size

               Object of
                Interest       Enhance




                Unwanted
                                Suppress
                Sidelobes



Classify “object types”     Optimize the receive aperture size
                       Experimental Results:
                    Tissue Mimicking Phantoms
        Azimuth
                            0         1X   2X
Range




                                            28.6 mm
                Original




                 –40           40        96.2 mm
         Adaptive Receive
            Aperture




                                           Dynamic range: 60 dB

				
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posted:11/25/2011
language:English
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