1 snark14.s170426 - A PICTURE RECONSTRUCTION PROGRAM
6 <*> MAP EM ALGORITHM FOR EMISSION TOMOGRAPHY. RECONSTRUCTION OF BRAIN
8 <*> PHANTOM. SIMULATING PET GEOMETRY WITH A RING OF 300 DETECTORS WITH
10 <*> EACH DETECTOR IN COINCIDENCE WITH 101 DETECTORS OPPOSITE IT.
12 <*> COEFFICIENT OF PENALTLY TERM IS SET TO 10.0
18 EXAMPLE 7 Brain Phantom
21 <#> SPECTRUM MONOCHROMATIC 511
22 energy spectrum is monochromatic at energy level 511
26 description of objects
28 numb type x-coord y-coord x-length y-length angle av dens 511
30 1 elip -7.0000 46.0000 3.0000 6.0000 17.0000 0.9500 0.9500
32 2 elip 7.0000 46.0000 3.0000 6.0000 -17.0000 1.0000 1.0000
34 3 rect -12.0000 64.0000 7.5000 4.5000 5.0000 1.0000 1.0000
36 4 rect 12.0000 64.0000 7.5000 4.5000 -5.0000 0.9500 0.9500
38 5 rect -38.0000 51.0000 3.5000 13.0000 -39.0000 0.9500 0.9500
40 6 rect 38.0000 51.0000 3.5000 13.0000 39.0000 1.0000 1.0000
42 7 rect -46.0000 24.0000 6.5000 6.0000 -18.0000 0.9500 0.9500
44 8 rect 46.0000 24.0000 6.5000 6.0000 18.0000 1.0000 1.0000
46 9 rect -49.0000 6.0000 2.5000 10.0000 63.0000 1.0000 1.0000
48 10 rect 49.0000 6.0000 2.5000 10.0000 -63.0000 0.9500 0.9500
50 11 rect -52.0000 -14.0000 9.0000 7.0000 -14.0000 0.9500 0.9500
52 12 rect 52.0000 -14.0000 9.0000 7.0000 14.0000 1.0000 1.0000
54 13 rect -10.0000 -56.0000 5.5000 10.0000 -1.0000 0.9500 0.9500
56 14 rect 10.0000 -56.0000 5.5000 10.0000 1.0000 1.0000 1.0000
58 15 elip -40.0000 -47.0000 9.0000 22.5000 48.0000 1.0000 1.0000
60 16 elip 40.0000 -47.0000 9.0000 22.5000 -48.0000 0.9500 0.9500
62 17 elip -8.0000 -22.0000 3.5000 15.5000 -9.0000 1.0000 1.0000
64 18 elip 8.0000 -22.0000 3.5000 15.5000 9.0000 0.9500 0.9500
66 19 elip -27.0000 -6.0000 5.5000 23.5000 -5.0000 0.9500 0.9500
68 20 elip 27.0000 -6.0000 5.5000 23.5000 5.0000 1.0000 1.0000
70 21 elip -25.0000 38.0000 6.5000 10.5000 -14.0000 1.0000 1.0000
72 22 elip 25.0000 38.0000 6.5000 10.5000 14.0000 0.9500 0.9500
74 23 rect -8.0000 32.0000 1.5000 6.5000 38.0000 1.0000 1.0000
76 24 rect 8.0000 32.0000 1.5000 6.5000 -38.0000 0.9500 0.9500
78 25 rect -8.0000 3.0000 1.0000 9.0000 -33.0000 0.9500 0.9500
80 26 rect 8.0000 3.0000 1.0000 9.0000 33.0000 1.0000 1.0000
82 27 elip 0.0000 0.0000 66.5000 74.0000 0.0000 1.0000 1.0000
84 scale factor multiplying object densities 0.5100
87 inhomogeneity set to 0.0500
91 this run will generate a phantom
92 density in each pixel is obtained as the average of 7 x 7 points
95 <#> 95 PIXELS OF SIZE 1.6
96 picture size 95 x 95, pixel size 1.6000
101 this run will generate projection data
102 projection data are calculated by dividing each ray interval into 1 substrips
104 with aperture (substrip) weights 1
110 <#> divergent arc 153 306
111 rays are divergent from point sources
112 source to origin distance 153.0000
113 the detectors lie on an arc with source to detector distance = 306.0000
116 <#> RAYS USER 101 DETECTOR SPACING 3.2
117 number of rays per projection 101
118 at detector spacing 3.2000
121 <#> ANGLES 300 EQUAL SPACING
122 total number of projections 300
124 projection angles 0.0000 1.2000 2.4000 3.6000 4.8000 6.0000 7.2000 8.4000 9.6000 10.8000
125 12.0000 13.2000 14.4000 15.6000 16.8000 18.0000 19.2000 20.4000 21.6000 22.8000
126 24.0000 25.2000 26.4000 27.6000 28.8000 30.0000 31.2000 32.4000 33.6000 34.8000
127 36.0000 37.2000 38.4000 39.6000 40.8000 42.0000 43.2000 44.4000 45.6000 46.8000
128 48.0000 49.2000 50.4000 51.6000 52.8000 54.0000 55.2000 56.4000 57.6000 58.8000
129 60.0000 61.2000 62.4000 63.6000 64.8000 66.0000 67.2000 68.4000 69.6000 70.8000
130 72.0000 73.2000 74.4000 75.6000 76.8000 78.0000 79.2000 80.4000 81.6000 82.8000
131 84.0000 85.2000 86.4000 87.6000 88.8000 90.0000 91.2000 92.4000 93.6000 94.8000
132 96.0000 97.2000 98.4000 99.6000 100.8000 102.0000 103.2000 104.4000 105.6000 106.8000
133 108.0000 109.2000 110.4000 111.6000 112.8000 114.0000 115.2000 116.4000 117.6000 118.8000
134 120.0000 121.2000 122.4000 123.6000 124.8000 126.0000 127.2000 128.4000 129.6000 130.8000
135 132.0000 133.2000 134.4000 135.6000 136.8000 138.0000 139.2000 140.4000 141.6000 142.8000
136 144.0000 145.2000 146.4000 147.6000 148.8000 150.0000 151.2000 152.4000 153.6000 154.8000
137 156.0000 157.2000 158.4000 159.6000 160.8000 162.0000 163.2000 164.4000 165.6000 166.8000
138 168.0000 169.2000 170.4000 171.6000 172.8000 174.0000 175.2000 176.4000 177.6000 178.8000
139 180.0000 181.2000 182.4000 183.6000 184.8000 186.0000 187.2000 188.4000 189.6000 190.8000
140 192.0000 193.2000 194.4000 195.6000 196.8000 198.0000 199.2000 200.4000 201.6000 202.8000
141 204.0000 205.2000 206.4000 207.6000 208.8000 210.0000 211.2000 212.4000 213.6000 214.8000
142 216.0000 217.2000 218.4000 219.6000 220.8000 222.0000 223.2000 224.4000 225.6000 226.8000
143 228.0000 229.2000 230.4000 231.6000 232.8000 234.0000 235.2000 236.4000 237.6000 238.8000
144 240.0000 241.2000 242.4000 243.6000 244.8000 246.0000 247.2000 248.4000 249.6000 250.8000
145 252.0000 253.2000 254.4000 255.6000 256.8000 258.0000 259.2000 260.4000 261.6000 262.8000
146 264.0000 265.2000 266.4000 267.6000 268.8000 270.0000 271.2000 272.4000 273.6000 274.8000
147 276.0000 277.2000 278.4000 279.6000 280.8000 282.0000 283.2000 284.4000 285.6000 286.8000
148 288.0000 289.2000 290.4000 291.6000 292.8000 294.0000 295.2000 296.4000 297.6000 298.8000
149 300.0000 301.2000 302.4000 303.6000 304.8000 306.0000 307.2000 308.4000 309.6000 310.8000
150 312.0000 313.2000 314.4000 315.6000 316.8000 318.0000 319.2000 320.4000 321.6000 322.8000
151 324.0000 325.2000 326.4000 327.6000 328.8000 330.0000 331.2000 332.4000 333.6000 334.8000
152 336.0000 337.2000 338.4000 339.6000 340.8000 342.0000 343.2000 344.4000 345.6000 346.8000
153 348.0000 349.2000 350.4000 351.6000 352.8000 354.0000 355.2000 356.4000 357.6000 358.8000
156 <#> MEASUREMENT NOISY
157 noise characteristics of projection data follow
158 nature characteristics
160 <#> QUANTUM 1.0 1.0 CALIBRATION 4
164 seed for random number generator is 0
170 background absorption 0.0000
174 0.025 seconds phantom creation
175 0.100 seconds projection data creation
176 0.125 seconds used for processing command crea
183 EXAMPLE 7 Brain Phantom
187 energy spectrum is monochromatic at energy level 511
191 description of objects
193 numb type x-coord y-coord x-length y-length angle av dens 511
195 1 elip -7.0000 46.0000 3.0000 6.0000 17.0000 0.4845 0.4845
197 2 elip 7.0000 46.0000 3.0000 6.0000 -17.0000 0.5100 0.5100
199 3 rect -12.0000 64.0000 7.5000 4.5000 5.0000 0.5100 0.5100
201 4 rect 12.0000 64.0000 7.5000 4.5000 -5.0000 0.4845 0.4845
203 5 rect -38.0000 51.0000 3.5000 13.0000 -39.0000 0.4845 0.4845
205 6 rect 38.0000 51.0000 3.5000 13.0000 39.0000 0.5100 0.5100
207 7 rect -46.0000 24.0000 6.5000 6.0000 -18.0000 0.4845 0.4845
209 8 rect 46.0000 24.0000 6.5000 6.0000 18.0000 0.5100 0.5100
211 9 rect -49.0000 6.0000 2.5000 10.0000 63.0000 0.5100 0.5100
213 10 rect 49.0000 6.0000 2.5000 10.0000 -63.0000 0.4845 0.4845
215 11 rect -52.0000 -14.0000 9.0000 7.0000 -14.0000 0.4845 0.4845
217 12 rect 52.0000 -14.0000 9.0000 7.0000 14.0000 0.5100 0.5100
219 13 rect -10.0000 -56.0000 5.5000 10.0000 -1.0000 0.4845 0.4845
221 14 rect 10.0000 -56.0000 5.5000 10.0000 1.0000 0.5100 0.5100
223 15 elip -40.0000 -47.0000 9.0000 22.5000 48.0000 0.5100 0.5100
225 16 elip 40.0000 -47.0000 9.0000 22.5000 -48.0000 0.4845 0.4845
227 17 elip -8.0000 -22.0000 3.5000 15.5000 -9.0000 0.5100 0.5100
229 18 elip 8.0000 -22.0000 3.5000 15.5000 9.0000 0.4845 0.4845
231 19 elip -27.0000 -6.0000 5.5000 23.5000 -5.0000 0.4845 0.4845
233 20 elip 27.0000 -6.0000 5.5000 23.5000 5.0000 0.5100 0.5100
235 21 elip -25.0000 38.0000 6.5000 10.5000 -14.0000 0.5100 0.5100
237 22 elip 25.0000 38.0000 6.5000 10.5000 14.0000 0.4845 0.4845
239 23 rect -8.0000 32.0000 1.5000 6.5000 38.0000 0.5100 0.5100
241 24 rect 8.0000 32.0000 1.5000 6.5000 -38.0000 0.4845 0.4845
243 25 rect -8.0000 3.0000 1.0000 9.0000 -33.0000 0.4845 0.4845
245 26 rect 8.0000 3.0000 1.0000 9.0000 33.0000 0.5100 0.5100
247 27 elip 0.0000 0.0000 66.5000 74.0000 0.0000 0.5100 0.5100
249 scale factor multiplying object densities 0.5100
252 inhomogeneity set to 0.0500
256 density in each pixel is obtained as the average of 7 x 7 points
259 <#> pixe 95 size 1.6000
260 picture size 95 x 95, pixel size 1.6000
263 EXAMPLE 7 Brain Phantom
264 0.000 seconds used for processing command pict
271 EXAMPLE 7 Brain Phantom
275 energy spectrum is monochromatic at energy level 511
279 description of objects
281 numb type x-coord y-coord x-length y-length angle av dens 511
283 1 elip -7.0000 46.0000 3.0000 6.0000 17.0000 0.4845 0.4845
285 2 elip 7.0000 46.0000 3.0000 6.0000 -17.0000 0.5100 0.5100
287 3 rect -12.0000 64.0000 7.5000 4.5000 5.0000 0.5100 0.5100
289 4 rect 12.0000 64.0000 7.5000 4.5000 -5.0000 0.4845 0.4845
291 5 rect -38.0000 51.0000 3.5000 13.0000 -39.0000 0.4845 0.4845
293 6 rect 38.0000 51.0000 3.5000 13.0000 39.0000 0.5100 0.5100
295 7 rect -46.0000 24.0000 6.5000 6.0000 -18.0000 0.4845 0.4845
297 8 rect 46.0000 24.0000 6.5000 6.0000 18.0000 0.5100 0.5100
299 9 rect -49.0000 6.0000 2.5000 10.0000 63.0000 0.5100 0.5100
301 10 rect 49.0000 6.0000 2.5000 10.0000 -63.0000 0.4845 0.4845
303 11 rect -52.0000 -14.0000 9.0000 7.0000 -14.0000 0.4845 0.4845
305 12 rect 52.0000 -14.0000 9.0000 7.0000 14.0000 0.5100 0.5100
307 13 rect -10.0000 -56.0000 5.5000 10.0000 -1.0000 0.4845 0.4845
309 14 rect 10.0000 -56.0000 5.5000 10.0000 1.0000 0.5100 0.5100
311 15 elip -40.0000 -47.0000 9.0000 22.5000 48.0000 0.5100 0.5100
313 16 elip 40.0000 -47.0000 9.0000 22.5000 -48.0000 0.4845 0.4845
315 17 elip -8.0000 -22.0000 3.5000 15.5000 -9.0000 0.5100 0.5100
317 18 elip 8.0000 -22.0000 3.5000 15.5000 9.0000 0.4845 0.4845
319 19 elip -27.0000 -6.0000 5.5000 23.5000 -5.0000 0.4845 0.4845
321 20 elip 27.0000 -6.0000 5.5000 23.5000 5.0000 0.5100 0.5100
323 21 elip -25.0000 38.0000 6.5000 10.5000 -14.0000 0.5100 0.5100
325 22 elip 25.0000 38.0000 6.5000 10.5000 14.0000 0.4845 0.4845
327 23 rect -8.0000 32.0000 1.5000 6.5000 38.0000 0.5100 0.5100
329 24 rect 8.0000 32.0000 1.5000 6.5000 -38.0000 0.4845 0.4845
331 25 rect -8.0000 3.0000 1.0000 9.0000 -33.0000 0.4845 0.4845
333 26 rect 8.0000 3.0000 1.0000 9.0000 33.0000 0.5100 0.5100
335 27 elip 0.0000 0.0000 66.5000 74.0000 0.0000 0.5100 0.5100
337 scale factor multiplying object densities 0.5100
340 inhomogeneity set to 0.0500
344 projection data are calculated by dividing each ray interval into 1 substrips
346 with aperture (substrip) weights 1
352 <#> dive arc source at 153.0000 det dist 306.0000
353 rays are divergent from point sources
354 source to origin distance 153.0000
355 the detectors lie on an arc with source to detector distance = 306.0000
358 <#> rays user 101 spacing 3.2000
359 number of rays per projection 101
360 snark computed number of rays 151
361 at detector spacing 3.2000
365 total number of projections 300
368 projection angles 0.0000 1.2000 2.4000 3.6000 4.8000 6.0000 7.2000 8.4000 9.6000 10.8000
369 12.0000 13.2000 14.4000 15.6000 16.8000 18.0000 19.2000 20.4000 21.6000 22.8000
370 24.0000 25.2000 26.4000 27.6000 28.8000 30.0000 31.2000 32.4000 33.6000 34.8000
371 36.0000 37.2000 38.4000 39.6000 40.8000 42.0000 43.2000 44.4000 45.6000 46.8000
372 48.0000 49.2000 50.4000 51.6000 52.8000 54.0000 55.2000 56.4000 57.6000 58.8000
373 60.0000 61.2000 62.4000 63.6000 64.8000 66.0000 67.2000 68.4000 69.6000 70.8000
374 72.0000 73.2000 74.4000 75.6000 76.8000 78.0000 79.2000 80.4000 81.6000 82.8000
375 84.0000 85.2000 86.4000 87.6000 88.8000 90.0000 91.2000 92.4000 93.6000 94.8000
376 96.0000 97.2000 98.4000 99.6000 100.8000 102.0000 103.2000 104.4000 105.6000 106.8000
377 108.0000 109.2000 110.4000 111.6000 112.8000 114.0000 115.2000 116.4000 117.6000 118.8000
378 120.0000 121.2000 122.4000 123.6000 124.8000 126.0000 127.2000 128.4000 129.6000 130.8000
379 132.0000 133.2000 134.4000 135.6000 136.8000 138.0000 139.2000 140.4000 141.6000 142.8000
380 144.0000 145.2000 146.4000 147.6000 148.8000 150.0000 151.2000 152.4000 153.6000 154.8000
381 156.0000 157.2000 158.4000 159.6000 160.8000 162.0000 163.2000 164.4000 165.6000 166.8000
382 168.0000 169.2000 170.4000 171.6000 172.8000 174.0000 175.2000 176.4000 177.6000 178.8000
383 180.0000 181.2000 182.4000 183.6000 184.8000 186.0000 187.2000 188.4000 189.6000 190.8000
384 192.0000 193.2000 194.4000 195.6000 196.8000 198.0000 199.2000 200.4000 201.6000 202.8000
385 204.0000 205.2000 206.4000 207.6000 208.8000 210.0000 211.2000 212.4000 213.6000 214.8000
386 216.0000 217.2000 218.4000 219.6000 220.8000 222.0000 223.2000 224.4000 225.6000 226.8000
387 228.0000 229.2000 230.4000 231.6000 232.8000 234.0000 235.2000 236.4000 237.6000 238.8000
388 240.0000 241.2000 242.4000 243.6000 244.8000 246.0000 247.2000 248.4000 249.6000 250.8000
389 252.0000 253.2000 254.4000 255.6000 256.8000 258.0000 259.2000 260.4000 261.6000 262.8000
390 264.0000 265.2000 266.4000 267.6000 268.8000 270.0000 271.2000 272.4000 273.6000 274.8000
391 276.0000 277.2000 278.4000 279.6000 280.8000 282.0000 283.2000 284.4000 285.6000 286.8000
392 288.0000 289.2000 290.4000 291.6000 292.8000 294.0000 295.2000 296.4000 297.6000 298.8000
393 300.0000 301.2000 302.4000 303.6000 304.8000 306.0000 307.2000 308.4000 309.6000 310.8000
394 312.0000 313.2000 314.4000 315.6000 316.8000 318.0000 319.2000 320.4000 321.6000 322.8000
395 324.0000 325.2000 326.4000 327.6000 328.8000 330.0000 331.2000 332.4000 333.6000 334.8000
396 336.0000 337.2000 338.4000 339.6000 340.8000 342.0000 343.2000 344.4000 345.6000 346.8000
397 348.0000 349.2000 350.4000 351.6000 352.8000 354.0000 355.2000 356.4000 357.6000 358.8000
401 noise characteristics of projection data follow
402 nature characteristics
404 <#> quan 1.0000 1.0000 cali 4
408 seed for random number generator is 0
414 background absorption 0.0000
416 estimate of totlen = 4263169.769963
417 estimate of totden = 2020362.000000
418 estimate of average density = 0.4739
420 EXAMPLE 7 Brain Phantom
421 0.012 seconds used for processing command proj
426 <#> STOP ITERATION 20
428 0.000 seconds used for processing command stop
433 <#> EXECUTE AVERAGE EMAP
435 Example 7 Illustrating the MAP EM algorithm for PET
437 <#> gamma is 10.0 EVAL
439 -----------------------------------------------------------
441 maximum a-posteriori probability expectation maximization
444 evaluation flag is set
446 -----------------------------------------------------------
448 algorithm executed in iteration 1
449 0.167 seconds for the execution of the algorithm
450 iteration 1 completed
451 0.167 seconds for this iteration
452 algorithm executed in iteration 2
453 0.096 seconds for the execution of the algorithm
454 iteration 2 completed
455 0.096 seconds for this iteration
456 algorithm executed in iteration 3
457 0.106 seconds for the execution of the algorithm
458 iteration 3 completed
459 0.106 seconds for this iteration
460 algorithm executed in iteration 4
461 0.097 seconds for the execution of the algorithm
462 iteration 4 completed
463 0.097 seconds for this iteration
464 algorithm executed in iteration 5
465 0.096 seconds for the execution of the algorithm
466 iteration 5 completed
467 0.096 seconds for this iteration
468 algorithm executed in iteration 6
469 0.097 seconds for the execution of the algorithm
470 iteration 6 completed
471 0.097 seconds for this iteration
472 algorithm executed in iteration 7
473 0.096 seconds for the execution of the algorithm
474 iteration 7 completed
475 0.097 seconds for this iteration
476 algorithm executed in iteration 8
477 0.097 seconds for the execution of the algorithm
478 iteration 8 completed
479 0.097 seconds for this iteration
480 algorithm executed in iteration 9
481 0.112 seconds for the execution of the algorithm
482 iteration 9 completed
483 0.112 seconds for this iteration
484 algorithm executed in iteration 10
485 0.116 seconds for the execution of the algorithm
486 iteration 10 completed
487 0.116 seconds for this iteration
488 algorithm executed in iteration 11
489 0.100 seconds for the execution of the algorithm
490 iteration 11 completed
491 0.100 seconds for this iteration
492 algorithm executed in iteration 12
493 0.106 seconds for the execution of the algorithm
494 iteration 12 completed
495 0.106 seconds for this iteration
496 algorithm executed in iteration 13
497 0.117 seconds for the execution of the algorithm
498 iteration 13 completed
499 0.117 seconds for this iteration
500 algorithm executed in iteration 14
501 0.115 seconds for the execution of the algorithm
502 iteration 14 completed
503 0.115 seconds for this iteration
504 algorithm executed in iteration 15
505 0.115 seconds for the execution of the algorithm
506 iteration 15 completed
507 0.115 seconds for this iteration
508 algorithm executed in iteration 16
509 0.109 seconds for the execution of the algorithm
510 iteration 16 completed
511 0.109 seconds for this iteration
512 algorithm executed in iteration 17
513 0.102 seconds for the execution of the algorithm
514 iteration 17 completed
515 0.102 seconds for this iteration
516 algorithm executed in iteration 18
517 0.089 seconds for the execution of the algorithm
518 iteration 18 completed
519 0.089 seconds for this iteration
520 algorithm executed in iteration 19
521 0.101 seconds for the execution of the algorithm
522 iteration 19 completed
523 0.101 seconds for this iteration
524 algorithm executed in iteration 20
525 0.099 seconds for the execution of the algorithm
526 reconstruction completed after iteration 20
527 0.099 seconds for this iteration
528 2.135 seconds for all iterations
529 2.183 seconds used for processing command exec