Convergence of ℓ2/3 Regularization for Sparse Signal Recovery

Lu Liu () and Di-Rong Chen ()
Additional contact information
Lu Liu: Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China
Di-Rong Chen: Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 04, 1-20

Abstract: In this paper, we consider the problem of finding the sparsest solution to underdetermined linear systems. Unlike the literatures which use the ℓ1 regularization to approximate the original problem, we consider the ℓ2/3 regularization which leads to a better approximation but a nonconvex, nonsmooth, and non-Lipschitz optimization problem. Through developing a fixed point representation theory associated with the two thirds thresholding operator for ℓ2/3 regularization solutions, we propose a fixed point iterative thresholding algorithm based on two thirds norm for solving the k-sparsity problems. Relying on the restricted isometry property, we provide subsequentional convergence guarantee for this fixed point iterative thresholding algorithm on recovering a sparse signal. By discussing the preferred regularization parameters and studying the phase diagram, we get an adequate and efficient algorithm for the high-dimensional sparse signal recovery. Finally, comparing with the existing algorithms, such as the standard ℓ1 minimization, the iterative reweighted ℓ2 minimization, the iterative reweighted ℓ1 minimization, and iterative Half thresholding algorithm, we display the results of the experiment which indicate that the two thirds norm fixed point iterative thresholding algorithm applied to sparse signal recovery and large scale imageries from noisy measurements can be accepted as an effective solver for ℓ2/3 regularization.

Keywords: Compressed sensing; ℓ2/3 regularization; two thirds thresholding operator; fixed point iterative thresholding algorithm; phase diagram (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0217595915500232
Access to full text is restricted to subscribers

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:wsi:apjorx:v:32:y:2015:i:04:n:s0217595915500232

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0217595915500232

Access Statistics for this article

Asia-Pacific Journal of Operational Research (APJOR) is currently edited by Gongyun Zhao

More articles in Asia-Pacific Journal of Operational Research (APJOR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().