A Generalized l1 Greedy Algorithm for Image Reconstruction in CT
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.
Zhu, Jiehua, Xiezhang Li.
"A Generalized l1 Greedy Algorithm for Image Reconstruction in CT."
Applied Mathematics and Computations, 219 (10): 5487-5494.