A Generalized l₁ Greedy Algorithm for Image Reconstruction in Computed Tomography
Document Type
Presentation
Presentation Date
1-9-2013
Abstract or Description
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. A numerical experiment is also given to illustrate the advantage of the new algorithm.
Sponsorship/Conference/Institution
Joint Mathematics Meetings (JMM)
Location
San Diego, CA
Recommended Citation
Zhu, Jiehua.
2013.
"A Generalized l₁ Greedy Algorithm for Image Reconstruction in Computed Tomography."
Department of Mathematical Sciences Faculty Presentations.
Presentation 562.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/562
