1 snark14.s170710 - 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 PERFECT
157 projection data are noiseless
163 background absorption 0.0000
167 0.031 seconds phantom creation
168 0.109 seconds projection data creation
169 0.141 seconds used for processing command crea
176 EXAMPLE 7 Brain Phantom
180 energy spectrum is monochromatic at energy level 511
184 description of objects
186 numb type x-coord y-coord x-length y-length angle av dens 511
188 1 elip -7.0000 46.0000 3.0000 6.0000 17.0000 0.4845 0.4845
190 2 elip 7.0000 46.0000 3.0000 6.0000 -17.0000 0.5100 0.5100
192 3 rect -12.0000 64.0000 7.5000 4.5000 5.0000 0.5100 0.5100
194 4 rect 12.0000 64.0000 7.5000 4.5000 -5.0000 0.4845 0.4845
196 5 rect -38.0000 51.0000 3.5000 13.0000 -39.0000 0.4845 0.4845
198 6 rect 38.0000 51.0000 3.5000 13.0000 39.0000 0.5100 0.5100
200 7 rect -46.0000 24.0000 6.5000 6.0000 -18.0000 0.4845 0.4845
202 8 rect 46.0000 24.0000 6.5000 6.0000 18.0000 0.5100 0.5100
204 9 rect -49.0000 6.0000 2.5000 10.0000 63.0000 0.5100 0.5100
206 10 rect 49.0000 6.0000 2.5000 10.0000 -63.0000 0.4845 0.4845
208 11 rect -52.0000 -14.0000 9.0000 7.0000 -14.0000 0.4845 0.4845
210 12 rect 52.0000 -14.0000 9.0000 7.0000 14.0000 0.5100 0.5100
212 13 rect -10.0000 -56.0000 5.5000 10.0000 -1.0000 0.4845 0.4845
214 14 rect 10.0000 -56.0000 5.5000 10.0000 1.0000 0.5100 0.5100
216 15 elip -40.0000 -47.0000 9.0000 22.5000 48.0000 0.5100 0.5100
218 16 elip 40.0000 -47.0000 9.0000 22.5000 -48.0000 0.4845 0.4845
220 17 elip -8.0000 -22.0000 3.5000 15.5000 -9.0000 0.5100 0.5100
222 18 elip 8.0000 -22.0000 3.5000 15.5000 9.0000 0.4845 0.4845
224 19 elip -27.0000 -6.0000 5.5000 23.5000 -5.0000 0.4845 0.4845
226 20 elip 27.0000 -6.0000 5.5000 23.5000 5.0000 0.5100 0.5100
228 21 elip -25.0000 38.0000 6.5000 10.5000 -14.0000 0.5100 0.5100
230 22 elip 25.0000 38.0000 6.5000 10.5000 14.0000 0.4845 0.4845
232 23 rect -8.0000 32.0000 1.5000 6.5000 38.0000 0.5100 0.5100
234 24 rect 8.0000 32.0000 1.5000 6.5000 -38.0000 0.4845 0.4845
236 25 rect -8.0000 3.0000 1.0000 9.0000 -33.0000 0.4845 0.4845
238 26 rect 8.0000 3.0000 1.0000 9.0000 33.0000 0.5100 0.5100
240 27 elip 0.0000 0.0000 66.5000 74.0000 0.0000 0.5100 0.5100
242 scale factor multiplying object densities 0.5100
245 inhomogeneity set to 0.0500
249 density in each pixel is obtained as the average of 7 x 7 points
252 <#> pixe 95 size 1.6000
253 picture size 95 x 95, pixel size 1.6000
256 EXAMPLE 7 Brain Phantom
257 0.000 seconds used for processing command pict
264 EXAMPLE 7 Brain Phantom
268 energy spectrum is monochromatic at energy level 511
272 description of objects
274 numb type x-coord y-coord x-length y-length angle av dens 511
276 1 elip -7.0000 46.0000 3.0000 6.0000 17.0000 0.4845 0.4845
278 2 elip 7.0000 46.0000 3.0000 6.0000 -17.0000 0.5100 0.5100
280 3 rect -12.0000 64.0000 7.5000 4.5000 5.0000 0.5100 0.5100
282 4 rect 12.0000 64.0000 7.5000 4.5000 -5.0000 0.4845 0.4845
284 5 rect -38.0000 51.0000 3.5000 13.0000 -39.0000 0.4845 0.4845
286 6 rect 38.0000 51.0000 3.5000 13.0000 39.0000 0.5100 0.5100
288 7 rect -46.0000 24.0000 6.5000 6.0000 -18.0000 0.4845 0.4845
290 8 rect 46.0000 24.0000 6.5000 6.0000 18.0000 0.5100 0.5100
292 9 rect -49.0000 6.0000 2.5000 10.0000 63.0000 0.5100 0.5100
294 10 rect 49.0000 6.0000 2.5000 10.0000 -63.0000 0.4845 0.4845
296 11 rect -52.0000 -14.0000 9.0000 7.0000 -14.0000 0.4845 0.4845
298 12 rect 52.0000 -14.0000 9.0000 7.0000 14.0000 0.5100 0.5100
300 13 rect -10.0000 -56.0000 5.5000 10.0000 -1.0000 0.4845 0.4845
302 14 rect 10.0000 -56.0000 5.5000 10.0000 1.0000 0.5100 0.5100
304 15 elip -40.0000 -47.0000 9.0000 22.5000 48.0000 0.5100 0.5100
306 16 elip 40.0000 -47.0000 9.0000 22.5000 -48.0000 0.4845 0.4845
308 17 elip -8.0000 -22.0000 3.5000 15.5000 -9.0000 0.5100 0.5100
310 18 elip 8.0000 -22.0000 3.5000 15.5000 9.0000 0.4845 0.4845
312 19 elip -27.0000 -6.0000 5.5000 23.5000 -5.0000 0.4845 0.4845
314 20 elip 27.0000 -6.0000 5.5000 23.5000 5.0000 0.5100 0.5100
316 21 elip -25.0000 38.0000 6.5000 10.5000 -14.0000 0.5100 0.5100
318 22 elip 25.0000 38.0000 6.5000 10.5000 14.0000 0.4845 0.4845
320 23 rect -8.0000 32.0000 1.5000 6.5000 38.0000 0.5100 0.5100
322 24 rect 8.0000 32.0000 1.5000 6.5000 -38.0000 0.4845 0.4845
324 25 rect -8.0000 3.0000 1.0000 9.0000 -33.0000 0.4845 0.4845
326 26 rect 8.0000 3.0000 1.0000 9.0000 33.0000 0.5100 0.5100
328 27 elip 0.0000 0.0000 66.5000 74.0000 0.0000 0.5100 0.5100
330 scale factor multiplying object densities 0.5100
333 inhomogeneity set to 0.0500
337 projection data are calculated by dividing each ray interval into 1 substrips
339 with aperture (substrip) weights 1
345 <#> dive arc source at 153.0000 det dist 306.0000
346 rays are divergent from point sources
347 source to origin distance 153.0000
348 the detectors lie on an arc with source to detector distance = 306.0000
351 <#> rays user 101 spacing 3.2000
352 number of rays per projection 101
353 snark computed number of rays 151
354 at detector spacing 3.2000
358 total number of projections 300
361 projection angles 0.0000 1.2000 2.4000 3.6000 4.8000 6.0000 7.2000 8.4000 9.6000 10.8000
362 12.0000 13.2000 14.4000 15.6000 16.8000 18.0000 19.2000 20.4000 21.6000 22.8000
363 24.0000 25.2000 26.4000 27.6000 28.8000 30.0000 31.2000 32.4000 33.6000 34.8000
364 36.0000 37.2000 38.4000 39.6000 40.8000 42.0000 43.2000 44.4000 45.6000 46.8000
365 48.0000 49.2000 50.4000 51.6000 52.8000 54.0000 55.2000 56.4000 57.6000 58.8000
366 60.0000 61.2000 62.4000 63.6000 64.8000 66.0000 67.2000 68.4000 69.6000 70.8000
367 72.0000 73.2000 74.4000 75.6000 76.8000 78.0000 79.2000 80.4000 81.6000 82.8000
368 84.0000 85.2000 86.4000 87.6000 88.8000 90.0000 91.2000 92.4000 93.6000 94.8000
369 96.0000 97.2000 98.4000 99.6000 100.8000 102.0000 103.2000 104.4000 105.6000 106.8000
370 108.0000 109.2000 110.4000 111.6000 112.8000 114.0000 115.2000 116.4000 117.6000 118.8000
371 120.0000 121.2000 122.4000 123.6000 124.8000 126.0000 127.2000 128.4000 129.6000 130.8000
372 132.0000 133.2000 134.4000 135.6000 136.8000 138.0000 139.2000 140.4000 141.6000 142.8000
373 144.0000 145.2000 146.4000 147.6000 148.8000 150.0000 151.2000 152.4000 153.6000 154.8000
374 156.0000 157.2000 158.4000 159.6000 160.8000 162.0000 163.2000 164.4000 165.6000 166.8000
375 168.0000 169.2000 170.4000 171.6000 172.8000 174.0000 175.2000 176.4000 177.6000 178.8000
376 180.0000 181.2000 182.4000 183.6000 184.8000 186.0000 187.2000 188.4000 189.6000 190.8000
377 192.0000 193.2000 194.4000 195.6000 196.8000 198.0000 199.2000 200.4000 201.6000 202.8000
378 204.0000 205.2000 206.4000 207.6000 208.8000 210.0000 211.2000 212.4000 213.6000 214.8000
379 216.0000 217.2000 218.4000 219.6000 220.8000 222.0000 223.2000 224.4000 225.6000 226.8000
380 228.0000 229.2000 230.4000 231.6000 232.8000 234.0000 235.2000 236.4000 237.6000 238.8000
381 240.0000 241.2000 242.4000 243.6000 244.8000 246.0000 247.2000 248.4000 249.6000 250.8000
382 252.0000 253.2000 254.4000 255.6000 256.8000 258.0000 259.2000 260.4000 261.6000 262.8000
383 264.0000 265.2000 266.4000 267.6000 268.8000 270.0000 271.2000 272.4000 273.6000 274.8000
384 276.0000 277.2000 278.4000 279.6000 280.8000 282.0000 283.2000 284.4000 285.6000 286.8000
385 288.0000 289.2000 290.4000 291.6000 292.8000 294.0000 295.2000 296.4000 297.6000 298.8000
386 300.0000 301.2000 302.4000 303.6000 304.8000 306.0000 307.2000 308.4000 309.6000 310.8000
387 312.0000 313.2000 314.4000 315.6000 316.8000 318.0000 319.2000 320.4000 321.6000 322.8000
388 324.0000 325.2000 326.4000 327.6000 328.8000 330.0000 331.2000 332.4000 333.6000 334.8000
389 336.0000 337.2000 338.4000 339.6000 340.8000 342.0000 343.2000 344.4000 345.6000 346.8000
390 348.0000 349.2000 350.4000 351.6000 352.8000 354.0000 355.2000 356.4000 357.6000 358.8000
394 projection data are noiseless
400 background absorption 0.0000
402 estimate of totlen = 4263169.769963
403 estimate of totden = 2020712.203355
404 estimate of average density = 0.4740
406 EXAMPLE 7 Brain Phantom
407 0.016 seconds used for processing command proj
412 <#> STOP ITERATION 20
414 0.000 seconds used for processing command stop
419 <#> EXECUTE AVERAGE EMAP
421 Example 7 Illustrating the MAP EM algorithm for PET
423 <#> gamma is 10.0 EVAL
425 -----------------------------------------------------------
427 maximum a-posteriori probability expectation maximization
430 evaluation flag is set
432 -----------------------------------------------------------
434 *** WARNING - There exist negative values in the projection data ***
435 *** Negative values set to 0.0 ***
436 algorithm executed in iteration 1
437 0.172 seconds for the execution of the algorithm
438 iteration 1 completed
439 0.172 seconds for this iteration
440 algorithm executed in iteration 2
441 0.062 seconds for the execution of the algorithm
442 iteration 2 completed
443 0.062 seconds for this iteration
444 algorithm executed in iteration 3
445 0.031 seconds for the execution of the algorithm
446 iteration 3 completed
447 0.031 seconds for this iteration
448 algorithm executed in iteration 4
449 0.094 seconds for the execution of the algorithm
450 iteration 4 completed
451 0.094 seconds for this iteration
452 algorithm executed in iteration 5
453 0.094 seconds for the execution of the algorithm
454 iteration 5 completed
455 0.094 seconds for this iteration
456 algorithm executed in iteration 6
457 0.047 seconds for the execution of the algorithm
458 iteration 6 completed
459 0.047 seconds for this iteration
460 algorithm executed in iteration 7
461 0.109 seconds for the execution of the algorithm
462 iteration 7 completed
463 0.109 seconds for this iteration
464 algorithm executed in iteration 8
465 0.047 seconds for the execution of the algorithm
466 iteration 8 completed
467 0.047 seconds for this iteration
468 algorithm executed in iteration 9
469 0.031 seconds for the execution of the algorithm
470 iteration 9 completed
471 0.031 seconds for this iteration
472 algorithm executed in iteration 10
473 0.031 seconds for the execution of the algorithm
474 iteration 10 completed
475 0.031 seconds for this iteration
476 algorithm executed in iteration 11
477 0.062 seconds for the execution of the algorithm
478 iteration 11 completed
479 0.062 seconds for this iteration
480 algorithm executed in iteration 12
481 0.094 seconds for the execution of the algorithm
482 iteration 12 completed
483 0.094 seconds for this iteration
484 algorithm executed in iteration 13
485 0.062 seconds for the execution of the algorithm
486 iteration 13 completed
487 0.062 seconds for this iteration
488 algorithm executed in iteration 14
489 0.031 seconds for the execution of the algorithm
490 iteration 14 completed
491 0.031 seconds for this iteration
492 algorithm executed in iteration 15
493 0.062 seconds for the execution of the algorithm
494 iteration 15 completed
495 0.062 seconds for this iteration
496 algorithm executed in iteration 16
497 0.078 seconds for the execution of the algorithm
498 iteration 16 completed
499 0.078 seconds for this iteration
500 algorithm executed in iteration 17
501 0.078 seconds for the execution of the algorithm
502 iteration 17 completed
503 0.078 seconds for this iteration
504 algorithm executed in iteration 18
505 0.062 seconds for the execution of the algorithm
506 iteration 18 completed
507 0.062 seconds for this iteration
508 algorithm executed in iteration 19
509 0.078 seconds for the execution of the algorithm
510 iteration 19 completed
511 0.078 seconds for this iteration
512 algorithm executed in iteration 20
513 0.062 seconds for the execution of the algorithm
514 reconstruction completed after iteration 20
515 0.062 seconds for this iteration
516 1.391 seconds for all iterations
517 1.453 seconds used for processing command exec