snark14.s170710 - A PICTURE RECONSTRUCTION PROGRAM <*> *******EXAMPLE 7 <*> MAP EM ALGORITHM FOR EMISSION TOMOGRAPHY. RECONSTRUCTION OF BRAIN <*> PHANTOM. SIMULATING PET GEOMETRY WITH A RING OF 300 DETECTORS WITH <*> EACH DETECTOR IN COINCIDENCE WITH 101 DETECTORS OPPOSITE IT. <*> COEFFICIENT OF PENALTLY TERM IS SET TO 10.0 <*> <#> CREATE EXAMPLE 7 Brain Phantom <#> SPECTRUM MONOCHROMATIC 511 energy spectrum is monochromatic at energy level 511 <#> OBJECTS description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 511 1 elip -7.0000 46.0000 3.0000 6.0000 17.0000 0.9500 0.9500 2 elip 7.0000 46.0000 3.0000 6.0000 -17.0000 1.0000 1.0000 3 rect -12.0000 64.0000 7.5000 4.5000 5.0000 1.0000 1.0000 4 rect 12.0000 64.0000 7.5000 4.5000 -5.0000 0.9500 0.9500 5 rect -38.0000 51.0000 3.5000 13.0000 -39.0000 0.9500 0.9500 6 rect 38.0000 51.0000 3.5000 13.0000 39.0000 1.0000 1.0000 7 rect -46.0000 24.0000 6.5000 6.0000 -18.0000 0.9500 0.9500 8 rect 46.0000 24.0000 6.5000 6.0000 18.0000 1.0000 1.0000 9 rect -49.0000 6.0000 2.5000 10.0000 63.0000 1.0000 1.0000 10 rect 49.0000 6.0000 2.5000 10.0000 -63.0000 0.9500 0.9500 11 rect -52.0000 -14.0000 9.0000 7.0000 -14.0000 0.9500 0.9500 12 rect 52.0000 -14.0000 9.0000 7.0000 14.0000 1.0000 1.0000 13 rect -10.0000 -56.0000 5.5000 10.0000 -1.0000 0.9500 0.9500 14 rect 10.0000 -56.0000 5.5000 10.0000 1.0000 1.0000 1.0000 15 elip -40.0000 -47.0000 9.0000 22.5000 48.0000 1.0000 1.0000 16 elip 40.0000 -47.0000 9.0000 22.5000 -48.0000 0.9500 0.9500 17 elip -8.0000 -22.0000 3.5000 15.5000 -9.0000 1.0000 1.0000 18 elip 8.0000 -22.0000 3.5000 15.5000 9.0000 0.9500 0.9500 19 elip -27.0000 -6.0000 5.5000 23.5000 -5.0000 0.9500 0.9500 20 elip 27.0000 -6.0000 5.5000 23.5000 5.0000 1.0000 1.0000 21 elip -25.0000 38.0000 6.5000 10.5000 -14.0000 1.0000 1.0000 22 elip 25.0000 38.0000 6.5000 10.5000 14.0000 0.9500 0.9500 23 rect -8.0000 32.0000 1.5000 6.5000 38.0000 1.0000 1.0000 24 rect 8.0000 32.0000 1.5000 6.5000 -38.0000 0.9500 0.9500 25 rect -8.0000 3.0000 1.0000 9.0000 -33.0000 0.9500 0.9500 26 rect 8.0000 3.0000 1.0000 9.0000 33.0000 1.0000 1.0000 27 elip 0.0000 0.0000 66.5000 74.0000 0.0000 1.0000 1.0000 scale factor multiplying object densities 0.5100 seed set to 1 inhomogeneity set to 0.0500 <#> PHANTOM AVERAGE 7 this run will generate a phantom density in each pixel is obtained as the average of 7 x 7 points <#> 95 PIXELS OF SIZE 1.6 picture size 95 x 95, pixel size 1.6000 <#> RAYSUM AVERAGE 1 this run will generate projection data projection data are calculated by dividing each ray interval into 1 substrips with aperture (substrip) weights 1 <#> GEOMETRY <#> divergent arc 153 306 rays are divergent from point sources source to origin distance 153.0000 the detectors lie on an arc with source to detector distance = 306.0000 <#> RAYS USER 101 DETECTOR SPACING 3.2 number of rays per projection 101 at detector spacing 3.2000 <#> ANGLES 300 EQUAL SPACING total number of projections 300 projection angles 0.0000 1.2000 2.4000 3.6000 4.8000 6.0000 7.2000 8.4000 9.6000 10.8000 12.0000 13.2000 14.4000 15.6000 16.8000 18.0000 19.2000 20.4000 21.6000 22.8000 24.0000 25.2000 26.4000 27.6000 28.8000 30.0000 31.2000 32.4000 33.6000 34.8000 36.0000 37.2000 38.4000 39.6000 40.8000 42.0000 43.2000 44.4000 45.6000 46.8000 48.0000 49.2000 50.4000 51.6000 52.8000 54.0000 55.2000 56.4000 57.6000 58.8000 60.0000 61.2000 62.4000 63.6000 64.8000 66.0000 67.2000 68.4000 69.6000 70.8000 72.0000 73.2000 74.4000 75.6000 76.8000 78.0000 79.2000 80.4000 81.6000 82.8000 84.0000 85.2000 86.4000 87.6000 88.8000 90.0000 91.2000 92.4000 93.6000 94.8000 96.0000 97.2000 98.4000 99.6000 100.8000 102.0000 103.2000 104.4000 105.6000 106.8000 108.0000 109.2000 110.4000 111.6000 112.8000 114.0000 115.2000 116.4000 117.6000 118.8000 120.0000 121.2000 122.4000 123.6000 124.8000 126.0000 127.2000 128.4000 129.6000 130.8000 132.0000 133.2000 134.4000 135.6000 136.8000 138.0000 139.2000 140.4000 141.6000 142.8000 144.0000 145.2000 146.4000 147.6000 148.8000 150.0000 151.2000 152.4000 153.6000 154.8000 156.0000 157.2000 158.4000 159.6000 160.8000 162.0000 163.2000 164.4000 165.6000 166.8000 168.0000 169.2000 170.4000 171.6000 172.8000 174.0000 175.2000 176.4000 177.6000 178.8000 180.0000 181.2000 182.4000 183.6000 184.8000 186.0000 187.2000 188.4000 189.6000 190.8000 192.0000 193.2000 194.4000 195.6000 196.8000 198.0000 199.2000 200.4000 201.6000 202.8000 204.0000 205.2000 206.4000 207.6000 208.8000 210.0000 211.2000 212.4000 213.6000 214.8000 216.0000 217.2000 218.4000 219.6000 220.8000 222.0000 223.2000 224.4000 225.6000 226.8000 228.0000 229.2000 230.4000 231.6000 232.8000 234.0000 235.2000 236.4000 237.6000 238.8000 240.0000 241.2000 242.4000 243.6000 244.8000 246.0000 247.2000 248.4000 249.6000 250.8000 252.0000 253.2000 254.4000 255.6000 256.8000 258.0000 259.2000 260.4000 261.6000 262.8000 264.0000 265.2000 266.4000 267.6000 268.8000 270.0000 271.2000 272.4000 273.6000 274.8000 276.0000 277.2000 278.4000 279.6000 280.8000 282.0000 283.2000 284.4000 285.6000 286.8000 288.0000 289.2000 290.4000 291.6000 292.8000 294.0000 295.2000 296.4000 297.6000 298.8000 300.0000 301.2000 302.4000 303.6000 304.8000 306.0000 307.2000 308.4000 309.6000 310.8000 312.0000 313.2000 314.4000 315.6000 316.8000 318.0000 319.2000 320.4000 321.6000 322.8000 324.0000 325.2000 326.4000 327.6000 328.8000 330.0000 331.2000 332.4000 333.6000 334.8000 336.0000 337.2000 338.4000 339.6000 340.8000 342.0000 343.2000 344.4000 345.6000 346.8000 348.0000 349.2000 350.4000 351.6000 352.8000 354.0000 355.2000 356.4000 357.6000 358.8000 <#> MEASUREMENT PERFECT projection data are noiseless <#> BACKGROUND 0.0 at levels 511 background absorption 0.0000 <#> RUN 0.014 seconds phantom creation 0.078 seconds projection data creation 0.093 seconds used for processing command crea <*> <#> PICTURE TEST EXAMPLE 7 Brain Phantom <#> spec mono 511 energy spectrum is monochromatic at energy level 511 <#> obje description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 511 1 elip -7.0000 46.0000 3.0000 6.0000 17.0000 0.4845 0.4845 2 elip 7.0000 46.0000 3.0000 6.0000 -17.0000 0.5100 0.5100 3 rect -12.0000 64.0000 7.5000 4.5000 5.0000 0.5100 0.5100 4 rect 12.0000 64.0000 7.5000 4.5000 -5.0000 0.4845 0.4845 5 rect -38.0000 51.0000 3.5000 13.0000 -39.0000 0.4845 0.4845 6 rect 38.0000 51.0000 3.5000 13.0000 39.0000 0.5100 0.5100 7 rect -46.0000 24.0000 6.5000 6.0000 -18.0000 0.4845 0.4845 8 rect 46.0000 24.0000 6.5000 6.0000 18.0000 0.5100 0.5100 9 rect -49.0000 6.0000 2.5000 10.0000 63.0000 0.5100 0.5100 10 rect 49.0000 6.0000 2.5000 10.0000 -63.0000 0.4845 0.4845 11 rect -52.0000 -14.0000 9.0000 7.0000 -14.0000 0.4845 0.4845 12 rect 52.0000 -14.0000 9.0000 7.0000 14.0000 0.5100 0.5100 13 rect -10.0000 -56.0000 5.5000 10.0000 -1.0000 0.4845 0.4845 14 rect 10.0000 -56.0000 5.5000 10.0000 1.0000 0.5100 0.5100 15 elip -40.0000 -47.0000 9.0000 22.5000 48.0000 0.5100 0.5100 16 elip 40.0000 -47.0000 9.0000 22.5000 -48.0000 0.4845 0.4845 17 elip -8.0000 -22.0000 3.5000 15.5000 -9.0000 0.5100 0.5100 18 elip 8.0000 -22.0000 3.5000 15.5000 9.0000 0.4845 0.4845 19 elip -27.0000 -6.0000 5.5000 23.5000 -5.0000 0.4845 0.4845 20 elip 27.0000 -6.0000 5.5000 23.5000 5.0000 0.5100 0.5100 21 elip -25.0000 38.0000 6.5000 10.5000 -14.0000 0.5100 0.5100 22 elip 25.0000 38.0000 6.5000 10.5000 14.0000 0.4845 0.4845 23 rect -8.0000 32.0000 1.5000 6.5000 38.0000 0.5100 0.5100 24 rect 8.0000 32.0000 1.5000 6.5000 -38.0000 0.4845 0.4845 25 rect -8.0000 3.0000 1.0000 9.0000 -33.0000 0.4845 0.4845 26 rect 8.0000 3.0000 1.0000 9.0000 33.0000 0.5100 0.5100 27 elip 0.0000 0.0000 66.5000 74.0000 0.0000 0.5100 0.5100 scale factor multiplying object densities 0.5100 seed set to 1 inhomogeneity set to 0.0500 <#> phan aver 7 density in each pixel is obtained as the average of 7 x 7 points <#> pixe 95 size 1.6000 picture size 95 x 95, pixel size 1.6000 test picture read EXAMPLE 7 Brain Phantom 0.003 seconds used for processing command pict <*> <#> PROJECTION REAL EXAMPLE 7 Brain Phantom <#> spec mono 511 energy spectrum is monochromatic at energy level 511 <#> obje description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 511 1 elip -7.0000 46.0000 3.0000 6.0000 17.0000 0.4845 0.4845 2 elip 7.0000 46.0000 3.0000 6.0000 -17.0000 0.5100 0.5100 3 rect -12.0000 64.0000 7.5000 4.5000 5.0000 0.5100 0.5100 4 rect 12.0000 64.0000 7.5000 4.5000 -5.0000 0.4845 0.4845 5 rect -38.0000 51.0000 3.5000 13.0000 -39.0000 0.4845 0.4845 6 rect 38.0000 51.0000 3.5000 13.0000 39.0000 0.5100 0.5100 7 rect -46.0000 24.0000 6.5000 6.0000 -18.0000 0.4845 0.4845 8 rect 46.0000 24.0000 6.5000 6.0000 18.0000 0.5100 0.5100 9 rect -49.0000 6.0000 2.5000 10.0000 63.0000 0.5100 0.5100 10 rect 49.0000 6.0000 2.5000 10.0000 -63.0000 0.4845 0.4845 11 rect -52.0000 -14.0000 9.0000 7.0000 -14.0000 0.4845 0.4845 12 rect 52.0000 -14.0000 9.0000 7.0000 14.0000 0.5100 0.5100 13 rect -10.0000 -56.0000 5.5000 10.0000 -1.0000 0.4845 0.4845 14 rect 10.0000 -56.0000 5.5000 10.0000 1.0000 0.5100 0.5100 15 elip -40.0000 -47.0000 9.0000 22.5000 48.0000 0.5100 0.5100 16 elip 40.0000 -47.0000 9.0000 22.5000 -48.0000 0.4845 0.4845 17 elip -8.0000 -22.0000 3.5000 15.5000 -9.0000 0.5100 0.5100 18 elip 8.0000 -22.0000 3.5000 15.5000 9.0000 0.4845 0.4845 19 elip -27.0000 -6.0000 5.5000 23.5000 -5.0000 0.4845 0.4845 20 elip 27.0000 -6.0000 5.5000 23.5000 5.0000 0.5100 0.5100 21 elip -25.0000 38.0000 6.5000 10.5000 -14.0000 0.5100 0.5100 22 elip 25.0000 38.0000 6.5000 10.5000 14.0000 0.4845 0.4845 23 rect -8.0000 32.0000 1.5000 6.5000 38.0000 0.5100 0.5100 24 rect 8.0000 32.0000 1.5000 6.5000 -38.0000 0.4845 0.4845 25 rect -8.0000 3.0000 1.0000 9.0000 -33.0000 0.4845 0.4845 26 rect 8.0000 3.0000 1.0000 9.0000 33.0000 0.5100 0.5100 27 elip 0.0000 0.0000 66.5000 74.0000 0.0000 0.5100 0.5100 scale factor multiplying object densities 0.5100 seed set to 1 inhomogeneity set to 0.0500 <#> rays aver 1 projection data are calculated by dividing each ray interval into 1 substrips with aperture (substrip) weights 1 <#> geom <#> dive arc source at 153.0000 det dist 306.0000 rays are divergent from point sources source to origin distance 153.0000 the detectors lie on an arc with source to detector distance = 306.0000 <#> rays user 101 spacing 3.2000 number of rays per projection 101 snark computed number of rays 151 at detector spacing 3.2000 <#> angl 300 total number of projections 300 projection angles 0.0000 1.2000 2.4000 3.6000 4.8000 6.0000 7.2000 8.4000 9.6000 10.8000 12.0000 13.2000 14.4000 15.6000 16.8000 18.0000 19.2000 20.4000 21.6000 22.8000 24.0000 25.2000 26.4000 27.6000 28.8000 30.0000 31.2000 32.4000 33.6000 34.8000 36.0000 37.2000 38.4000 39.6000 40.8000 42.0000 43.2000 44.4000 45.6000 46.8000 48.0000 49.2000 50.4000 51.6000 52.8000 54.0000 55.2000 56.4000 57.6000 58.8000 60.0000 61.2000 62.4000 63.6000 64.8000 66.0000 67.2000 68.4000 69.6000 70.8000 72.0000 73.2000 74.4000 75.6000 76.8000 78.0000 79.2000 80.4000 81.6000 82.8000 84.0000 85.2000 86.4000 87.6000 88.8000 90.0000 91.2000 92.4000 93.6000 94.8000 96.0000 97.2000 98.4000 99.6000 100.8000 102.0000 103.2000 104.4000 105.6000 106.8000 108.0000 109.2000 110.4000 111.6000 112.8000 114.0000 115.2000 116.4000 117.6000 118.8000 120.0000 121.2000 122.4000 123.6000 124.8000 126.0000 127.2000 128.4000 129.6000 130.8000 132.0000 133.2000 134.4000 135.6000 136.8000 138.0000 139.2000 140.4000 141.6000 142.8000 144.0000 145.2000 146.4000 147.6000 148.8000 150.0000 151.2000 152.4000 153.6000 154.8000 156.0000 157.2000 158.4000 159.6000 160.8000 162.0000 163.2000 164.4000 165.6000 166.8000 168.0000 169.2000 170.4000 171.6000 172.8000 174.0000 175.2000 176.4000 177.6000 178.8000 180.0000 181.2000 182.4000 183.6000 184.8000 186.0000 187.2000 188.4000 189.6000 190.8000 192.0000 193.2000 194.4000 195.6000 196.8000 198.0000 199.2000 200.4000 201.6000 202.8000 204.0000 205.2000 206.4000 207.6000 208.8000 210.0000 211.2000 212.4000 213.6000 214.8000 216.0000 217.2000 218.4000 219.6000 220.8000 222.0000 223.2000 224.4000 225.6000 226.8000 228.0000 229.2000 230.4000 231.6000 232.8000 234.0000 235.2000 236.4000 237.6000 238.8000 240.0000 241.2000 242.4000 243.6000 244.8000 246.0000 247.2000 248.4000 249.6000 250.8000 252.0000 253.2000 254.4000 255.6000 256.8000 258.0000 259.2000 260.4000 261.6000 262.8000 264.0000 265.2000 266.4000 267.6000 268.8000 270.0000 271.2000 272.4000 273.6000 274.8000 276.0000 277.2000 278.4000 279.6000 280.8000 282.0000 283.2000 284.4000 285.6000 286.8000 288.0000 289.2000 290.4000 291.6000 292.8000 294.0000 295.2000 296.4000 297.6000 298.8000 300.0000 301.2000 302.4000 303.6000 304.8000 306.0000 307.2000 308.4000 309.6000 310.8000 312.0000 313.2000 314.4000 315.6000 316.8000 318.0000 319.2000 320.4000 321.6000 322.8000 324.0000 325.2000 326.4000 327.6000 328.8000 330.0000 331.2000 332.4000 333.6000 334.8000 336.0000 337.2000 338.4000 339.6000 340.8000 342.0000 343.2000 344.4000 345.6000 346.8000 348.0000 349.2000 350.4000 351.6000 352.8000 354.0000 355.2000 356.4000 357.6000 358.8000 <#> meas perf projection data are noiseless <#> back 0.0000 at levels 511 background absorption 0.0000 estimate of totlen = 4263169.769963 estimate of totden = 2023083.983824 estimate of average density = 0.4745 projection data read EXAMPLE 7 Brain Phantom 0.017 seconds used for processing command proj <*> <#> STOP ITERATION 20 20 iterations 0.000 seconds used for processing command stop <*> <#> EXECUTE AVERAGE EMAP Example 7 Illustrating the MAP EM algorithm for PET <#> gamma is 10.0 EVAL ----------------------------------------------------------- maximum a-posteriori probability expectation maximization gamma: 10.000 evaluation flag is set ----------------------------------------------------------- *** WARNING - There exist negative values in the projection data *** *** Negative values set to 0.0 *** algorithm executed in iteration 1 0.063 seconds for the execution of the algorithm iteration 1 completed 0.064 seconds for this iteration algorithm executed in iteration 2 0.040 seconds for the execution of the algorithm iteration 2 completed 0.040 seconds for this iteration algorithm executed in iteration 3 0.040 seconds for the execution of the algorithm iteration 3 completed 0.040 seconds for this iteration algorithm executed in iteration 4 0.040 seconds for the execution of the algorithm iteration 4 completed 0.040 seconds for this iteration algorithm executed in iteration 5 0.041 seconds for the execution of the algorithm iteration 5 completed 0.041 seconds for this iteration algorithm executed in iteration 6 0.042 seconds for the execution of the algorithm iteration 6 completed 0.042 seconds for this iteration algorithm executed in iteration 7 0.044 seconds for the execution of the algorithm iteration 7 completed 0.044 seconds for this iteration algorithm executed in iteration 8 0.041 seconds for the execution of the algorithm iteration 8 completed 0.041 seconds for this iteration algorithm executed in iteration 9 0.040 seconds for the execution of the algorithm iteration 9 completed 0.040 seconds for this iteration algorithm executed in iteration 10 0.041 seconds for the execution of the algorithm iteration 10 completed 0.041 seconds for this iteration algorithm executed in iteration 11 0.040 seconds for the execution of the algorithm iteration 11 completed 0.040 seconds for this iteration algorithm executed in iteration 12 0.040 seconds for the execution of the algorithm iteration 12 completed 0.040 seconds for this iteration algorithm executed in iteration 13 0.040 seconds for the execution of the algorithm iteration 13 completed 0.040 seconds for this iteration algorithm executed in iteration 14 0.040 seconds for the execution of the algorithm iteration 14 completed 0.040 seconds for this iteration algorithm executed in iteration 15 0.040 seconds for the execution of the algorithm iteration 15 completed 0.040 seconds for this iteration algorithm executed in iteration 16 0.040 seconds for the execution of the algorithm iteration 16 completed 0.041 seconds for this iteration algorithm executed in iteration 17 0.040 seconds for the execution of the algorithm iteration 17 completed 0.040 seconds for this iteration algorithm executed in iteration 18 0.040 seconds for the execution of the algorithm iteration 18 completed 0.040 seconds for this iteration algorithm executed in iteration 19 0.041 seconds for the execution of the algorithm iteration 19 completed 0.041 seconds for this iteration algorithm executed in iteration 20 0.041 seconds for the execution of the algorithm reconstruction completed after iteration 20 0.041 seconds for this iteration 0.836 seconds for all iterations 0.883 seconds used for processing command exec <*> <#> END