A Smoothed - Norm and - Norm Regularization Algorithm for Computed Tomography

Jiehua Zhu and Xiezhang Li

Journal of Applied Mathematics, 2019, vol. 2019, 1-8

Abstract:

The nonmonotone alternating direction algorithm (NADA) was recently proposed for effectively solving a class of equality-constrained nonsmooth optimization problems and applied to the total variation minimization in image reconstruction, but the reconstructed images suffer from the artifacts. Though by the - norm regularization the edge can be effectively retained, the problem is NP hard. The smoothed - norm approximates the - norm as a limit of smooth convex functions and provides a smooth measure of sparsity in applications. The smoothed - norm regularization has been an attractive research topic in sparse image and signal recovery. In this paper, we present a combined smoothed - norm and - norm regularization algorithm using the NADA for image reconstruction in computed tomography. We resolve the computation challenge resulting from the smoothed - norm minimization. The numerical experiments demonstrate that the proposed algorithm improves the quality of the reconstructed images with the same cost of CPU time and reduces the computation time significantly while maintaining the same image quality compared with the - norm regularization in absence of the smoothed - norm.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/JAM/2019/8398035.pdf (application/pdf)
http://downloads.hindawi.com/journals/JAM/2019/8398035.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:8398035

DOI: 10.1155/2019/8398035

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().