Successive Concave Sparsity Approximation for Compressed Sensing
2016 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 64, no 21, 5657-5671 p.Article in journal (Refereed) Published
In this paper, based on a successively accuracy-increasing approximation of the l(0) norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the l(0) norm can be controlled. We prove that the series of the approximations asymptotically coincides with the l(1) and l(0) norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed that leads to a number of weighted l(1) minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms.
Place, publisher, year, edition, pages
2016. Vol. 64, no 21, 5657-5671 p.
Compressed sensing (CS), Iterative thresholding, Nonconvex optimization, Oracle estimator, The LASSO estimator
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-194254DOI: 10.1109/TSP.2016.2585096ISI: 000384291000016ScopusID: 2-s2.0-84990954599OAI: oai:DiVA.org:kth-194254DiVA: diva2:1039898
QC 201610252016-10-252016-10-212016-10-25Bibliographically approved