Illustrations of (a) forward–backward splitting-type optimization, and (b) our one-step proposed approach to solve the TV-based constrained convex optimization problem in Eq. (1).
Illustration of the computational processes required at each iteration for the four algorithms: (a) ASD-POCS, (b) STF, (c) GP-BL, and (d) GP-BB.
The reconstructed images of the Shepp-Logan phantom, using the respective four algorithms, as a function of 10, 30, and 50 iterations. A total of 40 projections in fan-beam geometry were used for the reconstructions.
Line profiles of the respective four algorithms with the (a) full line across the Shepp-Logan phantom, and (b) magnified view of the right one-third. The figure inset shows where the line profiles were generated.
Mean-squared relative percent error as a function of the number of iterations, for the respective four algorithms. The Shepp-Logan numerical phantom was used as the gold standard.
Spatial and contrast resolution slices of the reconstructed CatPhan 600 phantom using (a) FDK with 40 projections, (b) GP-BB with 40 projections in 12 iterations, and (c) FDK with 364 projections. The reconstruction times are listed on the figure.
A matrix view of the various image qualities achieved, using the GP-BB algorithm, as functions of number of projections and number of iterations, for the head-and-neck example patient. The window and level were kept the same for all images.
Selected images from Fig. 6; (a) FDK using 364 projections, (b) GP-BB with 12 iterations using 120 projections, (c) GP-BB with 18 iterations using 120 projections, (d) GP-BB with 24 iterations using 120 projections, and (f) GP-BB with 30 iterations using 364 projections. The reconstruction times are listed on the figure.
Computational time recorded to run 50 iterations.
List of the reconstruction times recorded for various projections and iterations tested.
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