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 ^l1 minimization problem: min||x||₁ subject to Ax=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.