snark14.s170426 - A PICTURE RECONSTRUCTION PROGRAM <*> EXAMPLE 5 <*> STAR PATTERN WITH 24 PARALLEL STRIP PROJECTIONS <*> RECONSTRUCTION BY ALL APPROPRIATE ALGORITHMS WITH DEFAULT <*> OR EASY OPTIONS. <*> <#> CREATE EXAMPLE 5 STAR PATTERN WITH 24 PARALLEL STRIP 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 <#> PARALLEL UNIFORM STRIP rays are parallel with uniform spacing between rays data collected along strips <#> RAYS USER 25 DETECTOR SPACING 2.0 number of rays per projection 25 at detector spacing 2.0000 <#> ANGLES 24 EQUAL SPACING total number of projections 24 projection angles 0.0000 7.5000 15.0000 22.5000 30.0000 37.5000 45.0000 52.5000 60.0000 67.5000 75.0000 82.5000 90.0000 97.5000 105.0000 112.5000 120.0000 127.5000 135.0000 142.5000 150.0000 157.5000 165.0000 172.5000 <#> 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 5 STAR PATTERN WITH 24 PARALLEL STRIP 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 5 STAR PATTERN WITH 24 PARALLEL STRIP PROJECTIONS 0.003 seconds used for processing command pict <*> <#> PROJECTION REAL EXAMPLE 5 STAR PATTERN WITH 24 PARALLEL STRIP 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 <#> para unif stri rays are parallel with uniform spacing between rays data collected along strips <#> rays user 25 spacing 2.0000 number of rays per projection 25 snark computed number of rays 37 at detector spacing 2.0000 <#> angl 24 total number of projections 24 projection angles 0.0000 7.5000 15.0000 22.5000 30.0000 37.5000 45.0000 52.5000 60.0000 67.5000 75.0000 82.5000 90.0000 97.5000 105.0000 112.5000 120.0000 127.5000 135.0000 142.5000 150.0000 157.5000 165.0000 172.5000 <#> meas perf projection data are noiseless <#> back 0.0000 at levels 10 background absorption 0.0000 estimate of totlen = 28263.966195 estimate of totden = 10749.116539 estimate of average density = 0.3803 projection data read EXAMPLE 5 STAR PATTERN WITH 24 PARALLEL STRIP PROJECTIONS 0.000 seconds used for processing command proj <*> <#> EXECUTE BACKPROJECTION EXAMPLE 5A CONTINUOUS BACKPROJECTION WITH LINEAR INTERPOLATION <#> CONTINUOUS 2 MULTIPLICATIVE continuous back-projection 2 order lagrange interpolation multiplicative normalization 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 0.000 seconds used for processing command exec <*> <#> EXECUTE CONVOLUTION EXAMPLE 5B CONVOLUTION WITH BANDLIMITING FILTER & LINEAR INTERPOLATION <#> BANDLIMITING 1.0 2 convolution reconstruction algorithm using filter band cutoff (or alpha) = 1.0000 2 point lagrange interpolation 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 0.004 seconds used for processing command exec <*> <#> EXECUTE RFL EXAMPLE 5C RHO FILTERED LAYERGRAM WITH BANDLIMITING FILTER & LINEAR INTERPOLATIO <#> BANDLIMITING 1.0 2 rho-filtered layergram reconstruction algorithm using filter band cutoff (or alpha) = 1.0000 2 point lagrange interpolation backprojection is performed on a 26 x 26 region 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 0.000 seconds used for processing command exec <*> <#> EXECUTE FOURIER EXAMPLE 5D FOURIER WITH BANDLIMITING FILTER & LINEAR INTERPOLATION f o u r i e r r e c o n s t r u c t i o n strip projections <#> BANDLIMITING 1.0 3 filter= 0 cutoff= 1.00 interp= 3 nsize1= 38 nsize2= 26 time for projection transforms : 0.000 seconds time for interpolations : 0.000 seconds time for backtransform : 0.000 seconds 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 0.000 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 5F ART WITH NO TRICKS <#> ART3 art3 method relaxation parameter is 1.0 norm is 2 tolerance is 0.0 <#> CONSTRAINT ART2 STEPS 888 constraint art2 way picture is not normalized 888 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 iteration 2 completed 0.000 seconds for this iteration algorithm executed in iteration 3 0.000 seconds for the execution of the algorithm iterative process stops at iteration 3 the change in variance is less than 0.006869 of the variance reconstruction completed after iteration 3 0.000 seconds for this iteration 0.000 seconds for all iterations 0.004 seconds used for processing command exec <*> <#> EXECUTE MART EXAMPLE 5G MULTIPLICATIVE ART A LA LENT <#> METHOD LENT 888 1.0 0.0 multiplicative art version lent no of rays used in each iteration 888 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 0.000 seconds for the execution of the algorithm iteration 1 completed 0.000 seconds for this iteration algorithm executed in iteration 2 0.004 seconds for the execution of the algorithm iterative process stops at iteration 2 the change in variance is less than 0.009779 of the variance reconstruction completed after iteration 2 0.004 seconds for this iteration 0.004 seconds for all iterations 0.007 seconds used for processing command exec <*> <#> EXECUTE QUADRATIC EXAMPLE 5H OPTIMIZATION OF LEAST SQUARES FUNCTIONAL USING CONJUGATE <#> 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 0.000 seconds for the execution of the algorithm iteration 1 completed 0.000 seconds for this iteration algorithm executed in iteration 2 0.003 seconds for the execution of the algorithm iteration 2 completed 0.003 seconds for this iteration algorithm executed in iteration 3 0.000 seconds for the execution of the algorithm iteration 3 completed 0.000 seconds for this iteration algorithm executed in iteration 4 0.000 seconds for the execution of the algorithm iteration 4 completed 0.000 seconds for this iteration algorithm executed in iteration 5 0.004 seconds for the execution of the algorithm iterative process stops at iteration 5 the change in variance is less than 0.095803 of the variance reconstruction completed after iteration 5 0.004 seconds for this iteration 0.007 seconds for all iterations 0.007 seconds used for processing command exec <*> <#> EXECUTE SIRT EXAMPLE 5I GENERALIZED SIMULTANEOUS ITERATIVE RECONSTRUCTION TECHNOLOGY user rays selected <#> METHOD GSIRT gsirt method sigma = inverse of relaxation = 1.0000 this run is unconstrained sirt this run is unnormalized sirt starting picture is as in execute command algorithm executed in iteration 1 0.003 seconds for the execution of the algorithm iteration 1 completed 0.003 seconds for this iteration algorithm executed in iteration 2 0.000 seconds for the execution of the algorithm iteration 2 completed 0.000 seconds for this iteration algorithm executed in iteration 3 0.000 seconds for the execution of the algorithm iteration 3 completed 0.000 seconds for this iteration algorithm executed in iteration 4 0.000 seconds for the execution of the algorithm iteration 4 completed 0.000 seconds for this iteration algorithm executed in iteration 5 0.000 seconds for the execution of the algorithm iteration 5 completed 0.000 seconds for this iteration algorithm executed in iteration 6 0.002 seconds for the execution of the algorithm iteration 6 completed 0.002 seconds for this iteration algorithm executed in iteration 7 0.000 seconds for the execution of the algorithm iteration 7 completed 0.000 seconds for this iteration algorithm executed in iteration 8 0.000 seconds for the execution of the algorithm iteration 8 completed 0.000 seconds for this iteration algorithm executed in iteration 9 0.000 seconds for the execution of the algorithm iteration 9 completed 0.000 seconds for this iteration algorithm executed in iteration 10 0.000 seconds for the execution of the algorithm iteration 10 completed 0.000 seconds for this iteration algorithm executed in iteration 11 0.002 seconds for the execution of the algorithm iteration 11 completed 0.002 seconds for this iteration algorithm executed in iteration 12 0.000 seconds for the execution of the algorithm iterative process stops at iteration 12 the change in variance is less than 0.086811 of the variance reconstruction completed after iteration 12 0.000 seconds for this iteration 0.008 seconds for all iterations 0.008 seconds used for processing command exec <*> <#> EVALUATE EXAMPLE 5 RECONSTRUCTION OF STAR PATTERN FROM PARALLEL 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 last iteration 0.003 seconds used for processing command eval <*> <#> END