- New Improved Penalty Methods for Sparse Reconstruction Based on Difference of Two Norms Yingnan Wang(wyn1982hotmail.com) Abstract: In this paper, we further establish two types of DC (Difference of Convex functions) programming for $l_0$ sparse reconstruction. Our DC objective functions are specified to the difference of two norms. One is the difference of $l_1$ and $l_{\sigma_q}$ norms (DC $l_1$-$l_{\sigma_q}$ for short) where $l_{\sigma_q}$ is the $l_1$ norm of the $q$-term ($q\geq1$) best approximation of a vector. Another one is the difference of $l_1$ and $l_r$ norms with $r>1$ (DC $l_1$-$l_r$ for short). The effectiveness of such special DC programs are illustrated and analyzed. Moreover, we designed two iterative algorithms for solving DC $l_1$-$l_{\sigma_q}$ and DC $l_1$-$l_{r}$ models, of which the first one is based on proximal gradient algorithm framework and in each subproblem we develop a closed form called generalized $q$-term shrinkage operator upon the special structure of $l_{\sigma_q}$ norm, and the second one is a majorized penalty method. Both of the convergent results are presented. The computational results demonstrate that the DC approaches of $l_1$-$l_{\sigma_q}$ model and $l_1$-$l_r$ model are very efficient and competitive ways in the aspects of sparsity and accuracy compared to $l_p$ model with $0 Keywords: compressed sensing, sparse approximation, exact recovery, difference of convex norms, non-convex and non-smooth, penalty method, proximal algorithm, majorization algorithm,$q\$-term shrinkage operator Category 1: Applications -- Science and Engineering Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares ) Category 3: Combinatorial Optimization (Approximation Algorithms ) Citation: Download: [PDF]Entry Submitted: 03/28/2015Entry Accepted: 03/29/2015Entry Last Modified: 03/28/2015Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.