1. PET/SPECT Phantom

2. Side View of Phantom

3. Image Resolution Intrinsic resolution FWHM Intrinsic resolution FWHM Field of view Field of view Measurement: A thin line source with F-18 is placed in a 20 cm phantom containing water as a scattering medium. The source is scanned and the images are reconstructed. A two dimensional Gaussian is filtered to the points surrounding the location of the source. The resolution at full width half maximum will be about 2.4 times the standard deviation parameter of the Gaussian distribution. The procedure is repeated with the source at different positions in the field of view. Measurement: A thin line source with F-18 is placed in a 20 cm phantom containing water as a scattering medium. The source is scanned and the images are reconstructed. A two dimensional Gaussian is filtered to the points surrounding the location of the source. The resolution at full width half maximum will be about 2.4 times the standard deviation parameter of the Gaussian distribution. The procedure is repeated with the source at different positions in the field of view. Axial resolution Axial resolution Measurement: A small point source is stepped through the imaging volume in small increments. For each step a scan of the source is made. The images are reconstructed, and a small region of interest is drawn around the location of the source. The measured activities in the ROI as a function of z-position is extracted from the series of images. Gaussians are fitted the points. The resolution in full width half maximum will be about 2.4 times the standard deviation parameter of the Gaussian distribution. The procedure is repeated with the source in different locations in the field of view. Measurement: A small point source is stepped through the imaging volume in small increments. For each step a scan of the source is made. The images are reconstructed, and a small region of interest is drawn around the location of the source. The measured activities in the ROI as a function of z-position is extracted from the series of images. Gaussians are fitted the points. The resolution in full width half maximum will be about 2.4 times the standard deviation parameter of the Gaussian distribution. The procedure is repeated with the source in different locations in the field of view.

4. Sensitivity A 20 cm cylinder phantom is filled with a water solution with an activity concentration of 0.1 µCurie per cc and placed in the center of the field of view. The sensitivity is defined as the true coincidence rate (i.e. scatter and randoms subtracted) divided by the activity concentration. A 20 cm cylinder phantom is filled with a water solution with an activity concentration of 0.1 µCurie per cc and placed in the center of the field of view. The sensitivity is defined as the true coincidence rate (i.e. scatter and randoms subtracted) divided by the activity concentration.

5. Timing Resolution Timing resolution FWHM: 5 ns Timing resolution FWHM: 5 ns The coincidence window is the time interval in which one event has to appear in order to be accepted in coincidence with another event. The coincidence window is the time interval in which one event has to appear in order to be accepted in coincidence with another event. The coincidence window is operator selector selectable to 8, 12 or 16 nanoseconds. 12 nanoseconds will give full efficiency. The coincidence window is operator selector selectable to 8, 12 or 16 nanoseconds. 12 nanoseconds will give full efficiency. 1.7 Linearity and random coincidences 1.7 Linearity and random coincidences The dead time is attributed to three components: detector dead time, the triple coincidence rate and the system dead time, the latter being of less importance. The dead time is attributed to three components: detector dead time, the triple coincidence rate and the system dead time, the latter being of less importance. The sources of the dead time are identified and measured with high precision. The sources of the dead time are identified and measured with high precision. The dead times are calculated with high accuracy, based on count rates, and corrections are made based on these calculations. The dead times do not impose limitations in usable count rates in our system. The dead times are calculated with high accuracy, based on count rates, and corrections are made based on these calculations. The dead times do not impose limitations in usable count rates in our system. The correction for the contribution of accidental coincidences is based on a high precision measurement of the coincidence time window. The accidental counts are then calculated with high accuracy and subtracted from the total coincidence counts. The correction for the contribution of accidental coincidences is based on a high precision measurement of the coincidence time window. The accidental counts are then calculated with high accuracy and subtracted from the total coincidence counts.

6. PET Phantom Images

7. The SINOGRAM Gamma Camera Example

8. Sinogram Formation in PET Coincidence events in PET scanner are categorized by plotting each LOR as function of its angular orientation versus its displacement from center of gantry. (A) Center of gantry is noted by cross (X), and locus of interest (e.g., tumor) is noted by ellipse. Four LORs passing through locus of interest are labeled A, B, C, and D. (B) These 4 LORs are plotted on this sinogram where angular orientation is on y-axis and displacement from center of gantry is on x-axis. If all possible LORs that pass through this point are plotted, it maps out half of sine wave turned on its side as shown here. (C) Sinograms of more complicated objects, such as sinogram of brain scan shown, are composed of many overlapping sine waves. (D) Reconstructed brain image corresponding to sinogram in (C) is shown. Coincidence events in PET scanner are categorized by plotting each LOR as function of its angular orientation versus its displacement from center of gantry. (A) Center of gantry is noted by cross (X), and locus of interest (e.g., tumor) is noted by ellipse. Four LORs passing through locus of interest are labeled A, B, C, and D. (B) These 4 LORs are plotted on this sinogram where angular orientation is on y-axis and displacement from center of gantry is on x-axis. If all possible LORs that pass through this point are plotted, it maps out half of sine wave turned on its side as shown here. (C) Sinograms of more complicated objects, such as sinogram of brain scan shown, are composed of many overlapping sine waves. (D) Reconstructed brain image corresponding to sinogram in (C) is shown.

9. Sinogram Formation in PET

10. Image Processing Digital Signal Processing Digital Signal Processing Direct Image Reconstruction Direct Image Reconstruction Sampling Theory Sampling Theory Fourier Analysis Fourier Analysis Image Filters Image Filters Mathematical Image Reconstruction Mathematical Image Reconstruction

11. Image Reconstruction  Direct Image Reconstruction  BackProjection  Algebraic Reconstruction

12. Time of Flight Systems Direct Image Reconstruction

13. Backprojection

14. Backprojection Animation

15. Sampling Theory A discrete “digital” image is a sampled image. A discrete “digital” image is a sampled image. Samples are taken from specific locations, usually a square (2-dimensional) array of elements, called pixels. Samples are taken from specific locations, usually a square (2-dimensional) array of elements, called pixels.

16. Sampling Theory continued, The idea is to obtain enough samples so that the essential information contained in the image is not lost. The idea is to obtain enough samples so that the essential information contained in the image is not lost. This can be proven mathematically, and is fundamental in communications theory, signal processing, electrical engineering, and other fields. This can be proven mathematically, and is fundamental in communications theory, signal processing, electrical engineering, and other fields.

17. Sampled Points: Discrete Function

18. Discrete function “Approximates” Continuous Function

19. Sampling The Information From The Heart Beat

20. More complicated sampling