snark14.s170426 - A PICTURE RECONSTRUCTION PROGRAM <*> EXAMPLE 6 <*> STAR PATTERN WITH 24 DIVERGENT PROJECTIONS <*> RECONSTRUCTION BY ALL APPROPRIATE ALGORITHMS WITH DEFAULT <*> OR EASY OPTIONS. <*> <#> CREATE EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS <#> SPECTRUM MONOCHROMATIC 10 energy spectrum is monochromatic at energy level 10 <#> OBJECTS description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 10 1 sect 0.0000 -24.0000 6.0000 24.0000 0.0000 1.0000 1.0000 2 sect 21.0000 -12.0000 6.0000 24.0000 60.0000 1.0000 1.0000 3 sect 21.0000 12.0000 6.0000 24.0000 120.0000 1.0000 1.0000 4 sect 0.0000 24.0000 6.0000 24.0000 180.0000 1.0000 1.0000 5 sect -21.0000 12.0000 6.0000 24.0000 240.0000 1.0000 1.0000 6 sect -21.0000 -12.0000 6.0000 24.0000 300.0000 1.0000 1.0000 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 <#> 25 PIXELS OF SIZE 2.0 picture size 25 x 25, pixel size 2.0000 <#> 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 <#> DIVERGENT ARC 40.0 40.0 rays are divergent from point sources source to origin distance 40.0000 the detectors lie on an arc with source to detector distance = 40.0000 <#> RAYS PROGRAM 25 2.0 DETECTOR SPACING 2.0 number of rays per projection 45 at detector spacing 2.0000 <#> ANGLES 24 EQUAL SPACING total number of projections 24 projection angles 0.0000 15.0000 30.0000 45.0000 60.0000 75.0000 90.0000 105.0000 120.0000 135.0000 150.0000 165.0000 180.0000 195.0000 210.0000 225.0000 240.0000 255.0000 270.0000 285.0000 300.0000 315.0000 330.0000 345.0000 <#> MEASUREMENT PERFECT projection data are noiseless <#> BACKGROUND 0.0 at levels 10 background absorption 0.0000 <#> RUN 0.000 seconds phantom creation 0.000 seconds projection data creation 0.000 seconds used for processing command crea <*> <#> PICTURE TEST EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS <#> spec mono 10 energy spectrum is monochromatic at energy level 10 <#> obje description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 10 1 sect 0.0000 -24.0000 6.0000 24.0000 0.0000 1.0000 1.0000 2 sect 21.0000 -12.0000 6.0000 24.0000 60.0000 1.0000 1.0000 3 sect 21.0000 12.0000 6.0000 24.0000 120.0000 1.0000 1.0000 4 sect 0.0000 24.0000 6.0000 24.0000 180.0000 1.0000 1.0000 5 sect -21.0000 12.0000 6.0000 24.0000 240.0000 1.0000 1.0000 6 sect -21.0000 -12.0000 6.0000 24.0000 300.0000 1.0000 1.0000 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 25 size 2.0000 picture size 25 x 25, pixel size 2.0000 test picture read EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS 0.002 seconds used for processing command pict <*> <#> PROJECTION REAL EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS <#> spec mono 10 energy spectrum is monochromatic at energy level 10 <#> obje description of objects density at levels numb type x-coord y-coord x-length y-length angle av dens 10 1 sect 0.0000 -24.0000 6.0000 24.0000 0.0000 1.0000 1.0000 2 sect 21.0000 -12.0000 6.0000 24.0000 60.0000 1.0000 1.0000 3 sect 21.0000 12.0000 6.0000 24.0000 120.0000 1.0000 1.0000 4 sect 0.0000 24.0000 6.0000 24.0000 180.0000 1.0000 1.0000 5 sect -21.0000 12.0000 6.0000 24.0000 240.0000 1.0000 1.0000 6 sect -21.0000 -12.0000 6.0000 24.0000 300.0000 1.0000 1.0000 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 <#> dive arc source at 40.0000 det dist 40.0000 rays are divergent from point sources source to origin distance 40.0000 the detectors lie on an arc with source to detector distance = 40.0000 <#> rays user 45 spacing 2.0000 number of rays per projection 45 snark computed number of rays 45 at detector spacing 2.0000 <#> angl 24 total number of projections 24 projection angles 0.0000 15.0000 30.0000 45.0000 60.0000 75.0000 90.0000 105.0000 120.0000 135.0000 150.0000 165.0000 180.0000 195.0000 210.0000 225.0000 240.0000 255.0000 270.0000 285.0000 300.0000 315.0000 330.0000 345.0000 <#> meas perf projection data are noiseless <#> back 0.0000 at levels 10 background absorption 0.0000 estimate of totlen = 32578.803295 estimate of totden = 11270.139500 estimate of average density = 0.3459 projection data read EXAMPLE 6 STAR PATTERN WITH 24 DIVERGENT PROJECTIONS 0.000 seconds used for processing command proj <*> <#> EXECUTE DCONV EXAMPLE 6A DIVERGENT BEAM CONVOLUTION WITH BANDLIMITING FILTER <#> 2 1 25 1.0 0 2 point lagrange interpolation one out of every 1 projection(s) used for reconstruction 25 points used on each side of convolution pre-smoothing weight on center ray = 1.0000 pre-smoothing weight on side rays = 0.0000 accurate back-projection <#> BANDLIMITING band-limiting filter total time for obtaining smoothed projection data was 0.000 total time for convoluting projection data was 0.000 total time for back-projecting was 0.000 algorithm executed in iteration 1 0.000 seconds for the execution of the algorithm reconstruction completed after iteration 1 0.000 seconds for this iteration 0.002 seconds used for processing command exec <*> <#> STOP TERMINATION VARIANCE = 0.1 termination test vari epsilon = 0.100000 0.000 seconds used for processing command stop <*> <#> EXECUTE ART EXAMPLE 6C ART WITH NO TRICKS <#> ART3 art3 method relaxation parameter is 1.0 norm is 2 tolerance is 0.0 <#> CONSTRAINT ART2 constraint art2 way relaxation constraints with cr = 1.0 picture is not normalized 1080 rays are used for each iteration algorithm executed in iteration 1 0.000 seconds for the execution of the algorithm iteration 1 completed 0.000 seconds for this iteration algorithm executed in iteration 2 0.000 seconds for the execution of the algorithm iterative process stops at iteration 2 the change in variance is less than 0.041353 of the variance reconstruction completed after iteration 2 0.000 seconds for this iteration 0.000 seconds for all iterations 0.002 seconds used for processing command exec <*> <#> EXECUTE MART EXAMPLE 6D MULTIPLICATIVE ART A LA LENT <#> METHOD LENT 0 1.0 0.0 multiplicative art version lent no of rays used in each iteration 1080 underrelaxation factor 1.00000 all projection data with values less than 1.0000000000e-20 are ignored reconstruction not normalized entropy functional not calculated algorithm executed in iteration 1 0.001 seconds for the execution of the algorithm iteration 1 completed 0.001 seconds for this iteration algorithm executed in iteration 2 0.001 seconds for the execution of the algorithm iterative process stops at iteration 2 the change in variance is less than 0.026757 of the variance reconstruction completed after iteration 2 0.001 seconds for this iteration 0.001 seconds for all iterations 0.002 seconds used for processing command exec <*> <#> EXECUTE QUADRATIC EXAMPLE 6E OPTIMIZATION OF LEAST SQUARES FUNCTIONAL USING CONJUGATE GRADIENT <#> 3 3 1 0 1 0.1 0.0 0.0 <#> 1 1 1 0 0 0 1.0 0.1 0 the conjugate gradient algorithm direct gradient computation ================================= algorithm executed in iteration 1 0.001 seconds for the execution of the algorithm iteration 1 completed 0.001 seconds for this iteration algorithm executed in iteration 2 0.002 seconds for the execution of the algorithm iteration 2 completed 0.002 seconds for this iteration algorithm executed in iteration 3 0.001 seconds for the execution of the algorithm iteration 3 completed 0.001 seconds for this iteration algorithm executed in iteration 4 0.001 seconds for the execution of the algorithm iteration 4 completed 0.001 seconds for this iteration algorithm executed in iteration 5 0.002 seconds for the execution of the algorithm iterative process stops at iteration 5 the change in variance is less than 0.046725 of the variance reconstruction completed after iteration 5 0.002 seconds for this iteration 0.005 seconds for all iterations 0.006 seconds used for processing command exec <*> <#> EVALUATE EXAMPLE 6 RECONSTRUCTION OF STAR PATTERN FROM DIVERGENT PROJECTIONS <#> WHOLEPIC Region cx cy u v ang t1 t2 wholepic -1e+20 1e+20 iterations 1 2 3 4 5 6 7 8 9 10 11 12 13 last iteration 0.002 seconds used for processing command eval <*> <#> END