1 snark14.s170426 - A PICTURE RECONSTRUCTION PROGRAM
6 <*> STAR PATTERN WITH 24 DIVERGENT PROJECTIONS
8 <*> RECONSTRUCTION BY ALL APPROPRIATE ALGORITHMS WITH DEFAULT
16 EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS
19 <#> SPECTRUM MONOCHROMATIC 10
20 energy spectrum is monochromatic at energy level 10
24 description of objects
26 numb type x-coord y-coord x-length y-length angle av dens 10
28 1 sect 0.0000 -24.0000 6.0000 24.0000 0.0000 1.0000 1.0000
30 2 sect 21.0000 -12.0000 6.0000 24.0000 60.0000 1.0000 1.0000
32 3 sect 21.0000 12.0000 6.0000 24.0000 120.0000 1.0000 1.0000
34 4 sect 0.0000 24.0000 6.0000 24.0000 180.0000 1.0000 1.0000
36 5 sect -21.0000 12.0000 6.0000 24.0000 240.0000 1.0000 1.0000
38 6 sect -21.0000 -12.0000 6.0000 24.0000 300.0000 1.0000 1.0000
40 scale factor multiplying object densities 1.0000
43 inhomogeneity set to 0.0000
47 this run will generate a phantom
48 density in each pixel is obtained as the average of 5 x 5 points
51 <#> 25 PIXELS OF SIZE 2.0
52 picture size 25 x 25, pixel size 2.0000
57 this run will generate projection data
58 projection data are calculated by dividing each ray interval into 1 substrips
60 with aperture (substrip) weights 1
66 <#> DIVERGENT ARC 40.0 40.0
67 rays are divergent from point sources
68 source to origin distance 40.0000
69 the detectors lie on an arc with source to detector distance = 40.0000
72 <#> RAYS PROGRAM 25 2.0 DETECTOR SPACING 2.0
73 number of rays per projection 45
74 at detector spacing 2.0000
77 <#> ANGLES 24 EQUAL SPACING
78 total number of projections 24
80 projection angles 0.0000 15.0000 30.0000 45.0000 60.0000 75.0000 90.0000 105.0000 120.0000 135.0000
81 150.0000 165.0000 180.0000 195.0000 210.0000 225.0000 240.0000 255.0000 270.0000 285.0000
82 300.0000 315.0000 330.0000 345.0000
85 <#> MEASUREMENT PERFECT
86 projection data are noiseless
92 background absorption 0.0000
96 0.000 seconds phantom creation
97 0.000 seconds projection data creation
98 0.000 seconds used for processing command crea
105 EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS
109 energy spectrum is monochromatic at energy level 10
113 description of objects
115 numb type x-coord y-coord x-length y-length angle av dens 10
117 1 sect 0.0000 -24.0000 6.0000 24.0000 0.0000 1.0000 1.0000
119 2 sect 21.0000 -12.0000 6.0000 24.0000 60.0000 1.0000 1.0000
121 3 sect 21.0000 12.0000 6.0000 24.0000 120.0000 1.0000 1.0000
123 4 sect 0.0000 24.0000 6.0000 24.0000 180.0000 1.0000 1.0000
125 5 sect -21.0000 12.0000 6.0000 24.0000 240.0000 1.0000 1.0000
127 6 sect -21.0000 -12.0000 6.0000 24.0000 300.0000 1.0000 1.0000
129 scale factor multiplying object densities 1.0000
132 inhomogeneity set to 0.0000
136 density in each pixel is obtained as the average of 5 x 5 points
139 <#> pixe 25 size 2.0000
140 picture size 25 x 25, pixel size 2.0000
143 EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS
144 0.002 seconds used for processing command pict
151 EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS
155 energy spectrum is monochromatic at energy level 10
159 description of objects
161 numb type x-coord y-coord x-length y-length angle av dens 10
163 1 sect 0.0000 -24.0000 6.0000 24.0000 0.0000 1.0000 1.0000
165 2 sect 21.0000 -12.0000 6.0000 24.0000 60.0000 1.0000 1.0000
167 3 sect 21.0000 12.0000 6.0000 24.0000 120.0000 1.0000 1.0000
169 4 sect 0.0000 24.0000 6.0000 24.0000 180.0000 1.0000 1.0000
171 5 sect -21.0000 12.0000 6.0000 24.0000 240.0000 1.0000 1.0000
173 6 sect -21.0000 -12.0000 6.0000 24.0000 300.0000 1.0000 1.0000
175 scale factor multiplying object densities 1.0000
178 inhomogeneity set to 0.0000
182 projection data are calculated by dividing each ray interval into 1 substrips
184 with aperture (substrip) weights 1
190 <#> dive arc source at 40.0000 det dist 40.0000
191 rays are divergent from point sources
192 source to origin distance 40.0000
193 the detectors lie on an arc with source to detector distance = 40.0000
196 <#> rays user 45 spacing 2.0000
197 number of rays per projection 45
198 snark computed number of rays 45
199 at detector spacing 2.0000
203 total number of projections 24
206 projection angles 0.0000 15.0000 30.0000 45.0000 60.0000 75.0000 90.0000 105.0000 120.0000 135.0000
207 150.0000 165.0000 180.0000 195.0000 210.0000 225.0000 240.0000 255.0000 270.0000 285.0000
208 300.0000 315.0000 330.0000 345.0000
212 projection data are noiseless
218 background absorption 0.0000
220 estimate of totlen = 32578.803295
221 estimate of totden = 11270.139500
222 estimate of average density = 0.3459
224 EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS
225 0.000 seconds used for processing command proj
232 EXAMPLE 6A DIVERGENT BEAM CONVOLUTION WITH BANDLIMITING FILTER
235 2 point lagrange interpolation
236 one out of every 1 projection(s) used for reconstruction
237 25 points used on each side of convolution
238 pre-smoothing weight on center ray = 1.0000
239 pre-smoothing weight on side rays = 0.0000
240 accurate back-projection
244 total time for obtaining smoothed projection data was 0.000
245 total time for convoluting projection data was 0.000
246 total time for back-projecting was 0.000
247 algorithm executed in iteration 1
248 0.000 seconds for the execution of the algorithm
249 reconstruction completed after iteration 1
250 0.000 seconds for this iteration
251 0.002 seconds used for processing command exec
256 <#> STOP TERMINATION VARIANCE = 0.1
257 termination test vari
259 0.000 seconds used for processing command stop
266 EXAMPLE 6C ART WITH NO TRICKS
270 relaxation parameter is 1.0
276 relaxation constraints with cr = 1.0
277 picture is not normalized
278 1080 rays are used for each iteration
279 algorithm executed in iteration 1
280 0.000 seconds for the execution of the algorithm
281 iteration 1 completed
282 0.000 seconds for this iteration
283 algorithm executed in iteration 2
284 0.000 seconds for the execution of the algorithm
285 iterative process stops at iteration 2
286 the change in variance is less than 0.041353 of the variance
287 reconstruction completed after iteration 2
288 0.000 seconds for this iteration
289 0.000 seconds for all iterations
290 0.002 seconds used for processing command exec
297 EXAMPLE 6D MULTIPLICATIVE ART A LA LENT
299 <#> METHOD LENT 0 1.0 0.0
300 multiplicative art version lent
301 no of rays used in each iteration 1080
302 underrelaxation factor 1.00000
303 all projection data with values less than 1.0000000000e-20 are ignored
304 reconstruction not normalized
305 entropy functional not calculated
306 algorithm executed in iteration 1
307 0.001 seconds for the execution of the algorithm
308 iteration 1 completed
309 0.001 seconds for this iteration
310 algorithm executed in iteration 2
311 0.001 seconds for the execution of the algorithm
312 iterative process stops at iteration 2
313 the change in variance is less than 0.026757 of the variance
314 reconstruction completed after iteration 2
315 0.001 seconds for this iteration
316 0.001 seconds for all iterations
317 0.002 seconds used for processing command exec
322 <#> EXECUTE QUADRATIC
324 EXAMPLE 6E OPTIMIZATION OF LEAST SQUARES FUNCTIONAL USING CONJUGATE GRADIENT
326 <#> 3 3 1 0 1 0.1 0.0 0.0
328 <#> 1 1 1 0 0 0 1.0 0.1 0
329 the conjugate gradient algorithm
331 direct gradient computation
332 =================================
333 algorithm executed in iteration 1
334 0.001 seconds for the execution of the algorithm
335 iteration 1 completed
336 0.001 seconds for this iteration
337 algorithm executed in iteration 2
338 0.002 seconds for the execution of the algorithm
339 iteration 2 completed
340 0.002 seconds for this iteration
341 algorithm executed in iteration 3
342 0.001 seconds for the execution of the algorithm
343 iteration 3 completed
344 0.001 seconds for this iteration
345 algorithm executed in iteration 4
346 0.001 seconds for the execution of the algorithm
347 iteration 4 completed
348 0.001 seconds for this iteration
349 algorithm executed in iteration 5
350 0.002 seconds for the execution of the algorithm
351 iterative process stops at iteration 5
352 the change in variance is less than 0.046725 of the variance
353 reconstruction completed after iteration 5
354 0.002 seconds for this iteration
355 0.005 seconds for all iterations
356 0.006 seconds used for processing command exec
363 EXAMPLE 6 RECONSTRUCTION OF STAR PATTERN FROM DIVERGENT PROJECTIONS
366 Region cx cy u v ang t1 t2
368 wholepic -1e+20 1e+20
370 iterations 1 2 3 4 5 6 7 8 9 10
374 0.002 seconds used for processing command eval