snark14.s170426 - A PICTURE RECONSTRUCTION PROGRAM <*> ******** EXAMPLE 8 <*> RECONSTRUCTION OF HEAD PHANTOM USING LINOGRAM AND FILTERED <*> BACKPROJECTION METHODS. SINC FILTER FOR LINOGRAM AND COSINE <*> FILTER FOR FBP. <*> <#> create EXAMPLE 8 LINOGRAM RECONSTRUCTION <#> spectrum monochromatic 75 energy spectrum is monochromatic at energy level 75 <#> objects cx cy u v ang den description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 75 1 elip 0.0000 0.0000 8.6250 6.4687 90.0000 0.4160 0.4160 2 elip 0.0000 0.0000 7.8750 5.7187 90.0000 -0.2060 -0.2060 3 elip 0.0000 1.5000 0.3750 0.3000 90.0000 -0.0030 -0.0030 4 elip 0.6750 -0.7500 0.2250 0.1500 140.0000 0.0100 0.0100 5 elip 0.7500 1.5000 0.3750 0.2250 50.0000 0.0030 0.0030 6 segm 1.3750 -7.5000 1.1000 0.6250 19.2000 -0.2040 -0.2040 7 segm 1.3750 -7.5000 1.1000 4.3200 19.2100 0.2040 0.2040 8 segm 0.0000 -2.2500 1.1250 0.3750 0.0000 -0.0030 -0.0030 9 segm 0.0000 -2.2500 1.1250 3.0000 0.0000 0.0030 0.0030 10 segm -1.0000 3.7500 1.0000 0.5000 135.0000 -0.0030 -0.0030 11 segm -1.0000 3.7500 1.0000 3.0000 135.0000 0.0030 0.0030 12 segm 1.0000 3.7500 1.0000 0.5000 225.0000 -0.0030 -0.0030 13 segm 1.0000 3.7500 1.0000 3.0000 225.0000 0.0030 0.0030 14 tria 5.0250 3.7500 1.1250 0.5000 110.7500 0.2060 0.2060 15 tria -5.0250 3.7500 1.1250 0.9000 -110.7500 0.2060 0.2060 scale factor multiplying object densities 1.0000 seed set to 0 inhomogeneity set to 0.0000 <#> phantom average 5 this run will generate a phantom density in each pixel is obtained as the average of 5 x 5 points <#> 115 0.1504 picture size 115 x 115, pixel size 0.1504 <#> 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 <#> linogram rays are parallel with variable spacing between rays data collected along lines number of rays per projection 231 at detector spacing 0.1504 total number of projections 462 projection angles 45.1243 45.3745 45.6268 45.8814 46.1382 46.3972 46.6584 46.9220 47.1878 47.4559 47.7263 47.9991 48.2742 48.5517 48.8316 49.1140 49.3987 49.6859 49.9756 50.2677 50.5623 50.8595 51.1592 51.4614 51.7662 52.0735 52.3835 52.6961 53.0112 53.3290 53.6495 53.9726 54.2984 54.6269 54.9581 55.2920 55.6285 55.9679 56.3099 56.6547 57.0023 57.3526 57.7057 58.0616 58.4202 58.7816 59.1458 59.5128 59.8826 60.2551 60.6305 61.0086 61.3895 61.7733 62.1597 62.5490 62.9410 63.3358 63.7334 64.1336 64.5367 64.9424 65.3508 65.7619 66.1757 66.5922 67.0113 67.4330 67.8573 68.2842 68.7136 69.1455 69.5800 70.0169 70.4562 70.8980 71.3421 71.7886 72.2373 72.6884 73.1416 73.5970 74.0546 74.5143 74.9760 75.4397 75.9054 76.3730 76.8425 77.3137 77.7867 78.2614 78.7378 79.2157 79.6952 80.1761 80.6584 81.1420 81.6270 82.1131 82.6004 83.0888 83.5782 84.0685 84.5597 85.0517 85.5444 86.0378 86.5318 87.0263 87.5212 88.0165 88.5121 89.0080 89.5039 90.0000 90.4961 90.9920 91.4879 91.9835 92.4788 92.9737 93.4682 93.9622 94.4556 94.9483 95.4403 95.9315 96.4218 96.9112 97.3996 97.8869 98.3730 98.8580 99.3416 99.8239 100.3048 100.7843 101.2622 101.7386 102.2133 102.6863 103.1575 103.6270 104.0946 104.5603 105.0240 105.4857 105.9454 106.4030 106.8584 107.3116 107.7627 108.2114 108.6579 109.1020 109.5438 109.9831 110.4200 110.8545 111.2864 111.7158 112.1427 112.5670 112.9887 113.4078 113.8243 114.2381 114.6492 115.0576 115.4633 115.8664 116.2666 116.6642 117.0590 117.4510 117.8403 118.2267 118.6105 118.9914 119.3695 119.7449 120.1174 120.4872 120.8542 121.2184 121.5798 121.9384 122.2943 122.6474 122.9977 123.3453 123.6901 124.0321 124.3715 124.7080 125.0419 125.3731 125.7016 126.0274 126.3505 126.6710 126.9888 127.3039 127.6165 127.9265 128.2338 128.5386 128.8408 129.1405 129.4377 129.7323 130.0244 130.3141 130.6013 130.8860 131.1684 131.4483 131.7258 132.0009 132.2737 132.5441 132.8122 133.0780 133.3416 133.6028 133.8618 134.1186 134.3732 134.6255 134.8757 135.1243 135.3745 135.6268 135.8814 136.1382 136.3972 136.6584 136.9220 137.1878 137.4559 137.7263 137.9991 138.2742 138.5517 138.8316 139.1140 139.3987 139.6859 139.9756 140.2677 140.5623 140.8595 141.1592 141.4614 141.7662 142.0735 142.3835 142.6961 143.0112 143.3290 143.6495 143.9726 144.2984 144.6269 144.9581 145.2920 145.6285 145.9679 146.3099 146.6547 147.0023 147.3526 147.7057 148.0616 148.4202 148.7816 149.1458 149.5128 149.8826 150.2551 150.6305 151.0086 151.3895 151.7733 152.1597 152.5490 152.9410 153.3358 153.7334 154.1336 154.5367 154.9424 155.3508 155.7619 156.1757 156.5922 157.0113 157.4330 157.8573 158.2842 158.7136 159.1455 159.5800 160.0169 160.4562 160.8980 161.3421 161.7886 162.2373 162.6884 163.1416 163.5970 164.0546 164.5143 164.9760 165.4397 165.9054 166.3730 166.8425 167.3137 167.7867 168.2614 168.7378 169.2157 169.6952 170.1761 170.6584 171.1420 171.6270 172.1131 172.6004 173.0888 173.5782 174.0685 174.5597 175.0517 175.5444 176.0378 176.5318 177.0263 177.5212 178.0165 178.5121 179.0080 179.5039 180.0000 180.4961 180.9920 181.4879 181.9835 182.4788 182.9737 183.4682 183.9622 184.4556 184.9483 185.4403 185.9315 186.4218 186.9112 187.3996 187.8869 188.3730 188.8580 189.3416 189.8239 190.3048 190.7843 191.2622 191.7386 192.2133 192.6863 193.1575 193.6270 194.0946 194.5603 195.0240 195.4857 195.9454 196.4030 196.8584 197.3116 197.7627 198.2114 198.6579 199.1020 199.5438 199.9831 200.4200 200.8545 201.2864 201.7158 202.1427 202.5670 202.9887 203.4078 203.8243 204.2381 204.6492 205.0576 205.4633 205.8664 206.2666 206.6642 207.0590 207.4510 207.8403 208.2267 208.6105 208.9914 209.3695 209.7449 210.1174 210.4872 210.8542 211.2184 211.5798 211.9384 212.2943 212.6474 212.9977 213.3453 213.6901 214.0321 214.3715 214.7080 215.0419 215.3731 215.7016 216.0274 216.3505 216.6710 216.9888 217.3039 217.6165 217.9265 218.2338 218.5386 218.8408 219.1405 219.4377 219.7323 220.0244 220.3141 220.6013 220.8860 221.1684 221.4483 221.7258 222.0009 222.2737 222.5441 222.8122 223.0780 223.3416 223.6028 223.8618 224.1186 224.3732 224.6255 224.8757 <#> measurement perfect projection data are noiseless <#> background absorption is 0.0 at levels 75 background absorption 0.0000 <#> run 0.024 seconds phantom creation 0.109 seconds projection data creation 0.135 seconds used for processing command crea <#> picture test EXAMPLE 8 LINOGRAM RECONSTRUCTION <#> spec mono 75 energy spectrum is monochromatic at energy level 75 <#> obje description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 75 1 elip 0.0000 0.0000 8.6250 6.4687 90.0000 0.4160 0.4160 2 elip 0.0000 0.0000 7.8750 5.7187 90.0000 -0.2060 -0.2060 3 elip 0.0000 1.5000 0.3750 0.3000 90.0000 -0.0030 -0.0030 4 elip 0.6750 -0.7500 0.2250 0.1500 140.0000 0.0100 0.0100 5 elip 0.7500 1.5000 0.3750 0.2250 50.0000 0.0030 0.0030 6 segm 1.3750 -7.5000 1.1000 0.6250 19.2000 -0.2040 -0.2040 7 segm 1.3750 -7.5000 1.1000 4.3200 19.2100 0.2040 0.2040 8 segm 0.0000 -2.2500 1.1250 0.3750 0.0000 -0.0030 -0.0030 9 segm 0.0000 -2.2500 1.1250 3.0000 0.0000 0.0030 0.0030 10 segm -1.0000 3.7500 1.0000 0.5000 135.0000 -0.0030 -0.0030 11 segm -1.0000 3.7500 1.0000 3.0000 135.0000 0.0030 0.0030 12 segm 1.0000 3.7500 1.0000 0.5000 225.0000 -0.0030 -0.0030 13 segm 1.0000 3.7500 1.0000 3.0000 225.0000 0.0030 0.0030 14 tria 5.0250 3.7500 1.1250 0.5000 110.7500 0.2060 0.2060 15 tria -5.0250 3.7500 1.1250 0.9000 -110.7500 0.2060 0.2060 scale factor multiplying object densities 1.0000 seed set to 0 inhomogeneity set to 0.0000 <#> phan aver 5 density in each pixel is obtained as the average of 5 x 5 points <#> pixe 115 size 0.1504 picture size 115 x 115, pixel size 0.1504 test picture read EXAMPLE 8 LINOGRAM RECONSTRUCTION 0.004 seconds used for processing command pict <#> projection real EXAMPLE 8 LINOGRAM RECONSTRUCTION <#> spec mono 75 energy spectrum is monochromatic at energy level 75 <#> obje description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 75 1 elip 0.0000 0.0000 8.6250 6.4687 90.0000 0.4160 0.4160 2 elip 0.0000 0.0000 7.8750 5.7187 90.0000 -0.2060 -0.2060 3 elip 0.0000 1.5000 0.3750 0.3000 90.0000 -0.0030 -0.0030 4 elip 0.6750 -0.7500 0.2250 0.1500 140.0000 0.0100 0.0100 5 elip 0.7500 1.5000 0.3750 0.2250 50.0000 0.0030 0.0030 6 segm 1.3750 -7.5000 1.1000 0.6250 19.2000 -0.2040 -0.2040 7 segm 1.3750 -7.5000 1.1000 4.3200 19.2100 0.2040 0.2040 8 segm 0.0000 -2.2500 1.1250 0.3750 0.0000 -0.0030 -0.0030 9 segm 0.0000 -2.2500 1.1250 3.0000 0.0000 0.0030 0.0030 10 segm -1.0000 3.7500 1.0000 0.5000 135.0000 -0.0030 -0.0030 11 segm -1.0000 3.7500 1.0000 3.0000 135.0000 0.0030 0.0030 12 segm 1.0000 3.7500 1.0000 0.5000 225.0000 -0.0030 -0.0030 13 segm 1.0000 3.7500 1.0000 3.0000 225.0000 0.0030 0.0030 14 tria 5.0250 3.7500 1.1250 0.5000 110.7500 0.2060 0.2060 15 tria -5.0250 3.7500 1.1250 0.9000 -110.7500 0.2060 0.2060 scale factor multiplying object densities 1.0000 seed set to 0 inhomogeneity set to 0.0000 <#> rays aver 1 projection data are calculated by dividing each ray interval into 1 substrips with aperture (substrip) weights 1 <#> geom <#> lino rays are parallel with variable spacing between rays data collected along lines number of rays per projection 231 snark computed number of rays 233 at detector spacing 0.1504 total number of projections 462 projection angles 45.1243 45.3745 45.6268 45.8814 46.1382 46.3972 46.6584 46.9220 47.1878 47.4559 47.7263 47.9991 48.2742 48.5517 48.8316 49.1140 49.3987 49.6859 49.9756 50.2677 50.5623 50.8595 51.1592 51.4614 51.7662 52.0735 52.3835 52.6961 53.0112 53.3290 53.6495 53.9726 54.2984 54.6269 54.9581 55.2920 55.6285 55.9679 56.3099 56.6547 57.0023 57.3526 57.7057 58.0616 58.4202 58.7816 59.1458 59.5128 59.8826 60.2551 60.6305 61.0086 61.3895 61.7733 62.1597 62.5490 62.9410 63.3358 63.7334 64.1336 64.5367 64.9424 65.3508 65.7619 66.1757 66.5922 67.0113 67.4330 67.8573 68.2842 68.7136 69.1455 69.5800 70.0169 70.4562 70.8980 71.3421 71.7886 72.2373 72.6884 73.1416 73.5970 74.0546 74.5143 74.9760 75.4397 75.9054 76.3730 76.8425 77.3137 77.7867 78.2614 78.7378 79.2157 79.6952 80.1761 80.6584 81.1420 81.6270 82.1131 82.6004 83.0888 83.5782 84.0685 84.5597 85.0517 85.5444 86.0378 86.5318 87.0263 87.5212 88.0165 88.5121 89.0080 89.5039 90.0000 90.4961 90.9920 91.4879 91.9835 92.4788 92.9737 93.4682 93.9622 94.4556 94.9483 95.4403 95.9315 96.4218 96.9112 97.3996 97.8869 98.3730 98.8580 99.3416 99.8239 100.3048 100.7843 101.2622 101.7386 102.2133 102.6863 103.1575 103.6270 104.0946 104.5603 105.0240 105.4857 105.9454 106.4030 106.8584 107.3116 107.7627 108.2114 108.6579 109.1020 109.5438 109.9831 110.4200 110.8545 111.2864 111.7158 112.1427 112.5670 112.9887 113.4078 113.8243 114.2381 114.6492 115.0576 115.4633 115.8664 116.2666 116.6642 117.0590 117.4510 117.8403 118.2267 118.6105 118.9914 119.3695 119.7449 120.1174 120.4872 120.8542 121.2184 121.5798 121.9384 122.2943 122.6474 122.9977 123.3453 123.6901 124.0321 124.3715 124.7080 125.0419 125.3731 125.7016 126.0274 126.3505 126.6710 126.9888 127.3039 127.6165 127.9265 128.2338 128.5386 128.8408 129.1405 129.4377 129.7323 130.0244 130.3141 130.6013 130.8860 131.1684 131.4483 131.7258 132.0009 132.2737 132.5441 132.8122 133.0780 133.3416 133.6028 133.8618 134.1186 134.3732 134.6255 134.8757 135.1243 135.3745 135.6268 135.8814 136.1382 136.3972 136.6584 136.9220 137.1878 137.4559 137.7263 137.9991 138.2742 138.5517 138.8316 139.1140 139.3987 139.6859 139.9756 140.2677 140.5623 140.8595 141.1592 141.4614 141.7662 142.0735 142.3835 142.6961 143.0112 143.3290 143.6495 143.9726 144.2984 144.6269 144.9581 145.2920 145.6285 145.9679 146.3099 146.6547 147.0023 147.3526 147.7057 148.0616 148.4202 148.7816 149.1458 149.5128 149.8826 150.2551 150.6305 151.0086 151.3895 151.7733 152.1597 152.5490 152.9410 153.3358 153.7334 154.1336 154.5367 154.9424 155.3508 155.7619 156.1757 156.5922 157.0113 157.4330 157.8573 158.2842 158.7136 159.1455 159.5800 160.0169 160.4562 160.8980 161.3421 161.7886 162.2373 162.6884 163.1416 163.5970 164.0546 164.5143 164.9760 165.4397 165.9054 166.3730 166.8425 167.3137 167.7867 168.2614 168.7378 169.2157 169.6952 170.1761 170.6584 171.1420 171.6270 172.1131 172.6004 173.0888 173.5782 174.0685 174.5597 175.0517 175.5444 176.0378 176.5318 177.0263 177.5212 178.0165 178.5121 179.0080 179.5039 180.0000 180.4961 180.9920 181.4879 181.9835 182.4788 182.9737 183.4682 183.9622 184.4556 184.9483 185.4403 185.9315 186.4218 186.9112 187.3996 187.8869 188.3730 188.8580 189.3416 189.8239 190.3048 190.7843 191.2622 191.7386 192.2133 192.6863 193.1575 193.6270 194.0946 194.5603 195.0240 195.4857 195.9454 196.4030 196.8584 197.3116 197.7627 198.2114 198.6579 199.1020 199.5438 199.9831 200.4200 200.8545 201.2864 201.7158 202.1427 202.5670 202.9887 203.4078 203.8243 204.2381 204.6492 205.0576 205.4633 205.8664 206.2666 206.6642 207.0590 207.4510 207.8403 208.2267 208.6105 208.9914 209.3695 209.7449 210.1174 210.4872 210.8542 211.2184 211.5798 211.9384 212.2943 212.6474 212.9977 213.3453 213.6901 214.0321 214.3715 214.7080 215.0419 215.3731 215.7016 216.0274 216.3505 216.6710 216.9888 217.3039 217.6165 217.9265 218.2338 218.5386 218.8408 219.1405 219.4377 219.7323 220.0244 220.3141 220.6013 220.8860 221.1684 221.4483 221.7258 222.0009 222.2737 222.5441 222.8122 223.0780 223.3416 223.6028 223.8618 224.1186 224.3732 224.6255 224.8757 <#> meas perf projection data are noiseless <#> back 0.0000 at levels 75 background absorption 0.0000 estimate of totlen = 1054747.357766 estimate of totden = 154874.529107 estimate of average density = 0.1468 projection data read EXAMPLE 8 LINOGRAM RECONSTRUCTION 0.048 seconds used for processing command proj <#> execute lino EXAMPLE 8a LINOGRAM METHOD <#> sinc 1.0 linogram reconstruction algorithm using filter sinc cutoff = 1.0000 algorithm executed in iteration 1 0.066 seconds for the execution of the algorithm reconstruction completed after iteration 1 0.066 seconds for this iteration 0.203 seconds used for processing command exec <#> execute conv EXAMPLE 8b FILTERED BACKPROJECTION <#> cosine 1.0 2 convolution reconstruction algorithm using filter cosi cutoff (or alpha) = 1.0000 2 point lagrange interpolation algorithm executed in iteration 1 0.113 seconds for the execution of the algorithm reconstruction completed after iteration 1 0.113 seconds for this iteration 0.246 seconds used for processing command exec <#> end