  Classical total variation (TV) based iterative reconstruction 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
few-view 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.
