Image Quality Lecture 2

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					                                       Image Quality
                                         Lecture 2

                                         Thomas Liu
                                UCSD Center for Functional MRI
                                   Resident Physics Course
                                        April 3, 2006




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                                         Topics

                Review MTF question
                Noise
                Receiver Operating Characteristics
                Sampling and Aliasing




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                                                                 1
                MTF = Fourier Transform (LTF)




                                       Bushberg et al 2001
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                                                             2
                             Noise and Image Quality




                                                              Bushberg et al 2001




                                                           Prince and Links 2005

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                                       What is Noise?
        Fluctuations in either the imaging system or the object
        being imaged.
        Quantization Noise: Due to conversion from analog
        waveform to digital number.
        Quantum Noise: Random fluctuation in the number of
        photons emitted and recorded.
        Thermal Noise: Random fluctuations present in all
        electronic systems. Also, sample noise in MRI
        Other types: flicker, burst, avalanche - observed in
        semiconductor devices.
        Structured Noise: physiological sources, interference

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                                                                                    3
                            Histograms and Distributions




                                         3rd grade heights     6th grade heights
                                                                    Bushberg et al 2001


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                                  Gaussian Distribution




                                                       Bushberg et al 2001

         1, 2, and 3 standard deviation intervals correspond to 68%,
         95%, and 99% of the observations
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                                                                                          4
                                              Poisson Process
                  Events occur at random instants of time at an average rate
                     of λ events per second.
                  Examples: arrival of customers to an ATM, emission of
                     photons from an x-ray source, lightning strikes in a
                     thunderstorm.


                       " = Average rate of events per second
                       "t = Average number of events at time t
                       "t = Variance in number of events



    ! Image Quality, T.T. Liu, Spring 2006




                                              Quantum Noise

                 For a Poisson process, the mean = variance, i.e. X = " 2
                 Therefore, the standard deviation is given by " = X

                 For X - ray systems, if the mean number of counts is N, then the
                standard deviation in the number of counts is " = N .


                            N
                 SNR =        = N.
                            "



!
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                                                                                    5
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                                                         Bushberg et al 2001


          Poisson Distribution describes x - ray counting statistics.
          Gaussian distribution is good approximation to Poisson when " = X


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!



                                                                               6
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                                       7
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                                       8
                                       Contrast Resolution




                                                             Bushberg et al 2001
                        Lower row shows effect of structure noise

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                                                                                   9
                                          TP
                     Sensitivity =
                                       TP + FN
                                    = Fraction of people who have the disease who test positive

                                          TN
                     Specificity =
                                       TN + FP
                                    = Fraction of people who do not have the disease who test negative

                                         TP
    Positive Predictive Value =
                                       TP + FP
                                    = Probability patient is actually abnormal when diagnosed as abnormal

                                          TN
    Negative Predictive Value =
                                       TN + FN
                                    = Probability patient is actually normal when diagnosed as normal.



!
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                                                        TP
                  True Positive Fraction =
                                                     TP + FN
                                                  = Sensitivity
                                                  = Probability of Detection


                                                       FP
                  False Positive Fraction =
                                                    FP + TN
                                                  =1-Specificity
                                                  = Probability of False Alarm



    !        Receiver operating characteristic (ROC) curve plots True
             Positive Fraction vs. False Positive Fraction


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                                                                                                            10
                                       Detection




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                                       Detection




                                       Area is a measure of detectability
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                                                                            11
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                                       12
                                             1
              Nyquist Frequency = FN =               Sampling Pitch
                                            2"
              If f > FN , then aliasing will occur



!




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                                                                      13
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                            Sampling in Image Space




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                                                      14
                                   Sampling in k-space




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                                                         15
                     Smoothing of Projections in CT

        Projection




        Beam                                     W= 2/(Δs)
        Width                                    δ=1/W= Δs/2
                                        2/(Δs)

       Smoothed
       Projection


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