A generalized l1 greedy algorithm for image reconstruction in CT

The sparse vector solutions for an underdetermined system of linear equations Ax=b have many applications in signal recovery and image reconstruction in tomography. Under certain conditions, the sparsest solution can be found by solving a constrained l(1) minimization problem: min parallel to x parallel to(1) subject to Ax = b. Recently, the reweighted l(1) minimization and l(1) greedy algorithm have been introduced to improve the convergence of the l(1) minimization problem. As an extension, a generalized l(1) greedy algorithm for computerized tomography (CT) is proposed in this paper. It is implemented as a generalized total variation minimization for images with sparse gradients in CT. Numerical experiments are also given to illustrate the advantage of the new algorithm. Published by Elsevier Inc.