1 snark14.s170426 - A PICTURE RECONSTRUCTION PROGRAM
6 <*> RECONSTRUCTION OF HEAD PHANTOM USING LINOGRAM AND FILTERED
8 <*> BACKPROJECTION METHODS. SINC FILTER FOR LINOGRAM AND COSINE
16 EXAMPLE 8 LINOGRAM RECONSTRUCTION
19 <#> spectrum monochromatic 75
20 energy spectrum is monochromatic at energy level 75
23 <#> objects cx cy u v ang den
24 description of objects
26 numb type x-coord y-coord x-length y-length angle av dens 75
28 1 elip 0.0000 0.0000 8.6250 6.4687 90.0000 0.4160 0.4160
30 2 elip 0.0000 0.0000 7.8750 5.7187 90.0000 -0.2060 -0.2060
32 3 elip 0.0000 1.5000 0.3750 0.3000 90.0000 -0.0030 -0.0030
34 4 elip 0.6750 -0.7500 0.2250 0.1500 140.0000 0.0100 0.0100
36 5 elip 0.7500 1.5000 0.3750 0.2250 50.0000 0.0030 0.0030
38 6 segm 1.3750 -7.5000 1.1000 0.6250 19.2000 -0.2040 -0.2040
40 7 segm 1.3750 -7.5000 1.1000 4.3200 19.2100 0.2040 0.2040
42 8 segm 0.0000 -2.2500 1.1250 0.3750 0.0000 -0.0030 -0.0030
44 9 segm 0.0000 -2.2500 1.1250 3.0000 0.0000 0.0030 0.0030
46 10 segm -1.0000 3.7500 1.0000 0.5000 135.0000 -0.0030 -0.0030
48 11 segm -1.0000 3.7500 1.0000 3.0000 135.0000 0.0030 0.0030
50 12 segm 1.0000 3.7500 1.0000 0.5000 225.0000 -0.0030 -0.0030
52 13 segm 1.0000 3.7500 1.0000 3.0000 225.0000 0.0030 0.0030
54 14 tria 5.0250 3.7500 1.1250 0.5000 110.7500 0.2060 0.2060
56 15 tria -5.0250 3.7500 1.1250 0.9000 -110.7500 0.2060 0.2060
58 scale factor multiplying object densities 1.0000
61 inhomogeneity set to 0.0000
65 this run will generate a phantom
66 density in each pixel is obtained as the average of 5 x 5 points
70 picture size 115 x 115, pixel size 0.1504
75 this run will generate projection data
76 projection data are calculated by dividing each ray interval into 1 substrips
78 with aperture (substrip) weights 1
85 rays are parallel with variable spacing between rays
86 data collected along lines
89 number of rays per projection 231
90 at detector spacing 0.1504
92 total number of projections 462
93 projection angles 45.1243 45.3745 45.6268 45.8814 46.1382 46.3972 46.6584 46.9220 47.1878 47.4559
94 47.7263 47.9991 48.2742 48.5517 48.8316 49.1140 49.3987 49.6859 49.9756 50.2677
95 50.5623 50.8595 51.1592 51.4614 51.7662 52.0735 52.3835 52.6961 53.0112 53.3290
96 53.6495 53.9726 54.2984 54.6269 54.9581 55.2920 55.6285 55.9679 56.3099 56.6547
97 57.0023 57.3526 57.7057 58.0616 58.4202 58.7816 59.1458 59.5128 59.8826 60.2551
98 60.6305 61.0086 61.3895 61.7733 62.1597 62.5490 62.9410 63.3358 63.7334 64.1336
99 64.5367 64.9424 65.3508 65.7619 66.1757 66.5922 67.0113 67.4330 67.8573 68.2842
100 68.7136 69.1455 69.5800 70.0169 70.4562 70.8980 71.3421 71.7886 72.2373 72.6884
101 73.1416 73.5970 74.0546 74.5143 74.9760 75.4397 75.9054 76.3730 76.8425 77.3137
102 77.7867 78.2614 78.7378 79.2157 79.6952 80.1761 80.6584 81.1420 81.6270 82.1131
103 82.6004 83.0888 83.5782 84.0685 84.5597 85.0517 85.5444 86.0378 86.5318 87.0263
104 87.5212 88.0165 88.5121 89.0080 89.5039 90.0000 90.4961 90.9920 91.4879 91.9835
105 92.4788 92.9737 93.4682 93.9622 94.4556 94.9483 95.4403 95.9315 96.4218 96.9112
106 97.3996 97.8869 98.3730 98.8580 99.3416 99.8239 100.3048 100.7843 101.2622 101.7386
107 102.2133 102.6863 103.1575 103.6270 104.0946 104.5603 105.0240 105.4857 105.9454 106.4030
108 106.8584 107.3116 107.7627 108.2114 108.6579 109.1020 109.5438 109.9831 110.4200 110.8545
109 111.2864 111.7158 112.1427 112.5670 112.9887 113.4078 113.8243 114.2381 114.6492 115.0576
110 115.4633 115.8664 116.2666 116.6642 117.0590 117.4510 117.8403 118.2267 118.6105 118.9914
111 119.3695 119.7449 120.1174 120.4872 120.8542 121.2184 121.5798 121.9384 122.2943 122.6474
112 122.9977 123.3453 123.6901 124.0321 124.3715 124.7080 125.0419 125.3731 125.7016 126.0274
113 126.3505 126.6710 126.9888 127.3039 127.6165 127.9265 128.2338 128.5386 128.8408 129.1405
114 129.4377 129.7323 130.0244 130.3141 130.6013 130.8860 131.1684 131.4483 131.7258 132.0009
115 132.2737 132.5441 132.8122 133.0780 133.3416 133.6028 133.8618 134.1186 134.3732 134.6255
116 134.8757 135.1243 135.3745 135.6268 135.8814 136.1382 136.3972 136.6584 136.9220 137.1878
117 137.4559 137.7263 137.9991 138.2742 138.5517 138.8316 139.1140 139.3987 139.6859 139.9756
118 140.2677 140.5623 140.8595 141.1592 141.4614 141.7662 142.0735 142.3835 142.6961 143.0112
119 143.3290 143.6495 143.9726 144.2984 144.6269 144.9581 145.2920 145.6285 145.9679 146.3099
120 146.6547 147.0023 147.3526 147.7057 148.0616 148.4202 148.7816 149.1458 149.5128 149.8826
121 150.2551 150.6305 151.0086 151.3895 151.7733 152.1597 152.5490 152.9410 153.3358 153.7334
122 154.1336 154.5367 154.9424 155.3508 155.7619 156.1757 156.5922 157.0113 157.4330 157.8573
123 158.2842 158.7136 159.1455 159.5800 160.0169 160.4562 160.8980 161.3421 161.7886 162.2373
124 162.6884 163.1416 163.5970 164.0546 164.5143 164.9760 165.4397 165.9054 166.3730 166.8425
125 167.3137 167.7867 168.2614 168.7378 169.2157 169.6952 170.1761 170.6584 171.1420 171.6270
126 172.1131 172.6004 173.0888 173.5782 174.0685 174.5597 175.0517 175.5444 176.0378 176.5318
127 177.0263 177.5212 178.0165 178.5121 179.0080 179.5039 180.0000 180.4961 180.9920 181.4879
128 181.9835 182.4788 182.9737 183.4682 183.9622 184.4556 184.9483 185.4403 185.9315 186.4218
129 186.9112 187.3996 187.8869 188.3730 188.8580 189.3416 189.8239 190.3048 190.7843 191.2622
130 191.7386 192.2133 192.6863 193.1575 193.6270 194.0946 194.5603 195.0240 195.4857 195.9454
131 196.4030 196.8584 197.3116 197.7627 198.2114 198.6579 199.1020 199.5438 199.9831 200.4200
132 200.8545 201.2864 201.7158 202.1427 202.5670 202.9887 203.4078 203.8243 204.2381 204.6492
133 205.0576 205.4633 205.8664 206.2666 206.6642 207.0590 207.4510 207.8403 208.2267 208.6105
134 208.9914 209.3695 209.7449 210.1174 210.4872 210.8542 211.2184 211.5798 211.9384 212.2943
135 212.6474 212.9977 213.3453 213.6901 214.0321 214.3715 214.7080 215.0419 215.3731 215.7016
136 216.0274 216.3505 216.6710 216.9888 217.3039 217.6165 217.9265 218.2338 218.5386 218.8408
137 219.1405 219.4377 219.7323 220.0244 220.3141 220.6013 220.8860 221.1684 221.4483 221.7258
138 222.0009 222.2737 222.5441 222.8122 223.0780 223.3416 223.6028 223.8618 224.1186 224.3732
142 <#> measurement perfect
143 projection data are noiseless
146 <#> background absorption is 0.0
149 background absorption 0.0000
153 0.024 seconds phantom creation
154 0.109 seconds projection data creation
155 0.135 seconds used for processing command crea
160 EXAMPLE 8 LINOGRAM RECONSTRUCTION
164 energy spectrum is monochromatic at energy level 75
168 description of objects
170 numb type x-coord y-coord x-length y-length angle av dens 75
172 1 elip 0.0000 0.0000 8.6250 6.4687 90.0000 0.4160 0.4160
174 2 elip 0.0000 0.0000 7.8750 5.7187 90.0000 -0.2060 -0.2060
176 3 elip 0.0000 1.5000 0.3750 0.3000 90.0000 -0.0030 -0.0030
178 4 elip 0.6750 -0.7500 0.2250 0.1500 140.0000 0.0100 0.0100
180 5 elip 0.7500 1.5000 0.3750 0.2250 50.0000 0.0030 0.0030
182 6 segm 1.3750 -7.5000 1.1000 0.6250 19.2000 -0.2040 -0.2040
184 7 segm 1.3750 -7.5000 1.1000 4.3200 19.2100 0.2040 0.2040
186 8 segm 0.0000 -2.2500 1.1250 0.3750 0.0000 -0.0030 -0.0030
188 9 segm 0.0000 -2.2500 1.1250 3.0000 0.0000 0.0030 0.0030
190 10 segm -1.0000 3.7500 1.0000 0.5000 135.0000 -0.0030 -0.0030
192 11 segm -1.0000 3.7500 1.0000 3.0000 135.0000 0.0030 0.0030
194 12 segm 1.0000 3.7500 1.0000 0.5000 225.0000 -0.0030 -0.0030
196 13 segm 1.0000 3.7500 1.0000 3.0000 225.0000 0.0030 0.0030
198 14 tria 5.0250 3.7500 1.1250 0.5000 110.7500 0.2060 0.2060
200 15 tria -5.0250 3.7500 1.1250 0.9000 -110.7500 0.2060 0.2060
202 scale factor multiplying object densities 1.0000
205 inhomogeneity set to 0.0000
209 density in each pixel is obtained as the average of 5 x 5 points
212 <#> pixe 115 size 0.1504
213 picture size 115 x 115, pixel size 0.1504
216 EXAMPLE 8 LINOGRAM RECONSTRUCTION
217 0.004 seconds used for processing command pict
222 EXAMPLE 8 LINOGRAM RECONSTRUCTION
226 energy spectrum is monochromatic at energy level 75
230 description of objects
232 numb type x-coord y-coord x-length y-length angle av dens 75
234 1 elip 0.0000 0.0000 8.6250 6.4687 90.0000 0.4160 0.4160
236 2 elip 0.0000 0.0000 7.8750 5.7187 90.0000 -0.2060 -0.2060
238 3 elip 0.0000 1.5000 0.3750 0.3000 90.0000 -0.0030 -0.0030
240 4 elip 0.6750 -0.7500 0.2250 0.1500 140.0000 0.0100 0.0100
242 5 elip 0.7500 1.5000 0.3750 0.2250 50.0000 0.0030 0.0030
244 6 segm 1.3750 -7.5000 1.1000 0.6250 19.2000 -0.2040 -0.2040
246 7 segm 1.3750 -7.5000 1.1000 4.3200 19.2100 0.2040 0.2040
248 8 segm 0.0000 -2.2500 1.1250 0.3750 0.0000 -0.0030 -0.0030
250 9 segm 0.0000 -2.2500 1.1250 3.0000 0.0000 0.0030 0.0030
252 10 segm -1.0000 3.7500 1.0000 0.5000 135.0000 -0.0030 -0.0030
254 11 segm -1.0000 3.7500 1.0000 3.0000 135.0000 0.0030 0.0030
256 12 segm 1.0000 3.7500 1.0000 0.5000 225.0000 -0.0030 -0.0030
258 13 segm 1.0000 3.7500 1.0000 3.0000 225.0000 0.0030 0.0030
260 14 tria 5.0250 3.7500 1.1250 0.5000 110.7500 0.2060 0.2060
262 15 tria -5.0250 3.7500 1.1250 0.9000 -110.7500 0.2060 0.2060
264 scale factor multiplying object densities 1.0000
267 inhomogeneity set to 0.0000
271 projection data are calculated by dividing each ray interval into 1 substrips
273 with aperture (substrip) weights 1
280 rays are parallel with variable spacing between rays
281 data collected along lines
284 number of rays per projection 231
285 snark computed number of rays 233
286 at detector spacing 0.1504
288 total number of projections 462
289 projection angles 45.1243 45.3745 45.6268 45.8814 46.1382 46.3972 46.6584 46.9220 47.1878 47.4559
290 47.7263 47.9991 48.2742 48.5517 48.8316 49.1140 49.3987 49.6859 49.9756 50.2677
291 50.5623 50.8595 51.1592 51.4614 51.7662 52.0735 52.3835 52.6961 53.0112 53.3290
292 53.6495 53.9726 54.2984 54.6269 54.9581 55.2920 55.6285 55.9679 56.3099 56.6547
293 57.0023 57.3526 57.7057 58.0616 58.4202 58.7816 59.1458 59.5128 59.8826 60.2551
294 60.6305 61.0086 61.3895 61.7733 62.1597 62.5490 62.9410 63.3358 63.7334 64.1336
295 64.5367 64.9424 65.3508 65.7619 66.1757 66.5922 67.0113 67.4330 67.8573 68.2842
296 68.7136 69.1455 69.5800 70.0169 70.4562 70.8980 71.3421 71.7886 72.2373 72.6884
297 73.1416 73.5970 74.0546 74.5143 74.9760 75.4397 75.9054 76.3730 76.8425 77.3137
298 77.7867 78.2614 78.7378 79.2157 79.6952 80.1761 80.6584 81.1420 81.6270 82.1131
299 82.6004 83.0888 83.5782 84.0685 84.5597 85.0517 85.5444 86.0378 86.5318 87.0263
300 87.5212 88.0165 88.5121 89.0080 89.5039 90.0000 90.4961 90.9920 91.4879 91.9835
301 92.4788 92.9737 93.4682 93.9622 94.4556 94.9483 95.4403 95.9315 96.4218 96.9112
302 97.3996 97.8869 98.3730 98.8580 99.3416 99.8239 100.3048 100.7843 101.2622 101.7386
303 102.2133 102.6863 103.1575 103.6270 104.0946 104.5603 105.0240 105.4857 105.9454 106.4030
304 106.8584 107.3116 107.7627 108.2114 108.6579 109.1020 109.5438 109.9831 110.4200 110.8545
305 111.2864 111.7158 112.1427 112.5670 112.9887 113.4078 113.8243 114.2381 114.6492 115.0576
306 115.4633 115.8664 116.2666 116.6642 117.0590 117.4510 117.8403 118.2267 118.6105 118.9914
307 119.3695 119.7449 120.1174 120.4872 120.8542 121.2184 121.5798 121.9384 122.2943 122.6474
308 122.9977 123.3453 123.6901 124.0321 124.3715 124.7080 125.0419 125.3731 125.7016 126.0274
309 126.3505 126.6710 126.9888 127.3039 127.6165 127.9265 128.2338 128.5386 128.8408 129.1405
310 129.4377 129.7323 130.0244 130.3141 130.6013 130.8860 131.1684 131.4483 131.7258 132.0009
311 132.2737 132.5441 132.8122 133.0780 133.3416 133.6028 133.8618 134.1186 134.3732 134.6255
312 134.8757 135.1243 135.3745 135.6268 135.8814 136.1382 136.3972 136.6584 136.9220 137.1878
313 137.4559 137.7263 137.9991 138.2742 138.5517 138.8316 139.1140 139.3987 139.6859 139.9756
314 140.2677 140.5623 140.8595 141.1592 141.4614 141.7662 142.0735 142.3835 142.6961 143.0112
315 143.3290 143.6495 143.9726 144.2984 144.6269 144.9581 145.2920 145.6285 145.9679 146.3099
316 146.6547 147.0023 147.3526 147.7057 148.0616 148.4202 148.7816 149.1458 149.5128 149.8826
317 150.2551 150.6305 151.0086 151.3895 151.7733 152.1597 152.5490 152.9410 153.3358 153.7334
318 154.1336 154.5367 154.9424 155.3508 155.7619 156.1757 156.5922 157.0113 157.4330 157.8573
319 158.2842 158.7136 159.1455 159.5800 160.0169 160.4562 160.8980 161.3421 161.7886 162.2373
320 162.6884 163.1416 163.5970 164.0546 164.5143 164.9760 165.4397 165.9054 166.3730 166.8425
321 167.3137 167.7867 168.2614 168.7378 169.2157 169.6952 170.1761 170.6584 171.1420 171.6270
322 172.1131 172.6004 173.0888 173.5782 174.0685 174.5597 175.0517 175.5444 176.0378 176.5318
323 177.0263 177.5212 178.0165 178.5121 179.0080 179.5039 180.0000 180.4961 180.9920 181.4879
324 181.9835 182.4788 182.9737 183.4682 183.9622 184.4556 184.9483 185.4403 185.9315 186.4218
325 186.9112 187.3996 187.8869 188.3730 188.8580 189.3416 189.8239 190.3048 190.7843 191.2622
326 191.7386 192.2133 192.6863 193.1575 193.6270 194.0946 194.5603 195.0240 195.4857 195.9454
327 196.4030 196.8584 197.3116 197.7627 198.2114 198.6579 199.1020 199.5438 199.9831 200.4200
328 200.8545 201.2864 201.7158 202.1427 202.5670 202.9887 203.4078 203.8243 204.2381 204.6492
329 205.0576 205.4633 205.8664 206.2666 206.6642 207.0590 207.4510 207.8403 208.2267 208.6105
330 208.9914 209.3695 209.7449 210.1174 210.4872 210.8542 211.2184 211.5798 211.9384 212.2943
331 212.6474 212.9977 213.3453 213.6901 214.0321 214.3715 214.7080 215.0419 215.3731 215.7016
332 216.0274 216.3505 216.6710 216.9888 217.3039 217.6165 217.9265 218.2338 218.5386 218.8408
333 219.1405 219.4377 219.7323 220.0244 220.3141 220.6013 220.8860 221.1684 221.4483 221.7258
334 222.0009 222.2737 222.5441 222.8122 223.0780 223.3416 223.6028 223.8618 224.1186 224.3732
339 projection data are noiseless
345 background absorption 0.0000
347 estimate of totlen = 1054747.357766
348 estimate of totden = 154874.529107
349 estimate of average density = 0.1468
351 EXAMPLE 8 LINOGRAM RECONSTRUCTION
352 0.048 seconds used for processing command proj
357 EXAMPLE 8a LINOGRAM METHOD
360 linogram reconstruction algorithm
363 algorithm executed in iteration 1
364 0.066 seconds for the execution of the algorithm
365 reconstruction completed after iteration 1
366 0.066 seconds for this iteration
367 0.203 seconds used for processing command exec
372 EXAMPLE 8b FILTERED BACKPROJECTION
375 convolution reconstruction algorithm
377 cutoff (or alpha) = 1.0000
378 2 point lagrange interpolation
379 algorithm executed in iteration 1
380 0.113 seconds for the execution of the algorithm
381 reconstruction completed after iteration 1
382 0.113 seconds for this iteration
383 0.246 seconds used for processing command exec