A Generalized l1 Greedy Algorithm for Image Reconstruction in CT

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Applied Mathematics and Computations




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 l1 minimization problem: min||x||1 subject toAx=b. Recently, the reweighted l1 minimization and l1 greedy algorithm have been introduced to improve the convergence of the l1 minimization problem. As an extension, a generalized l1 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.