Group Sparsity based Sparse-Sampling CT Reconstruction.

Classical total variation (TV) based iterative re-construction algorithms assume that the signal is piecewise smooth, which causes reconstruction results to suffer from the over-smoothing effect. To address this problem, this work presents a novel computed tomography (CT) reconstruction method for the sparse-sampling problem called the group- sparsity regularization-based simultaneous algebraic reconstruction technique (GSR-SART). Group-based sparse representation, which utilizes the concept of a group as the basic unit of sparse representation instead of a patch, is introduced as the image domain prior regularization term to eliminate the over-smoothing effect. By grouping the nonlocal patches into different clusters with similarity measured by Euclidean distance, the sparsity and nonlocal similarity in a single image are simultaneously explored. The split Bregman iteration algorithm is applied to obtain the numerical scheme. Experimental results demonstrate that our method both qualitatively and quantitatively outperforms several existing reconstruction methods, including filtered back projection, expectation maximization, SART, and TV-based projections onto convex sets.