Accession Number:

ADA561005

Title:

Verifiable and Computable Performance Analysis of Sparsity Recovery

Descriptive Note:

Conference paper

Corporate Author:

WASHINGTON UNIV ST LOUIS MO DEPT OF ELECTRICAL AND SYSTEMS ENGINEERING

Personal Author(s):

• Tang, Gongguo
• Nehorai, Arye

Report Date:

2011-10-05

Pagination or Media Count:

28.0

Abstract:

In this paper, we develop verifiable and computable performance analysis of sparsity recovery. We define a family of goodness measures for arbitrary sensing matrices as a set of optimization problems, and design algorithms with a theoretical global convergence guarantee to compute these goodness measures. The proposed algorithms solve a series of second-order cone programs, or linear programs. As a by-product, we implement an efficient algorithm to verify a sufficient condition for exact sparsity recovery in the noise-free case. We derive performance bounds on the recovery errors in terms of these goodness measures. We also analytically demonstrate that the developed goodness measures are non-degenerate for a large class of random sensing matrices, as long as the number of measurements is relatively large. Numerical experiments show that, compared with the restricted isometry based performance bounds, our error bounds apply to a wider range of problems and are tighter, when the sparsity levels of the signals are relatively low.

Descriptors:

• *ALGORITHMS
• CONVERGENCE
• LINEAR PROGRAMMING
• SYMPOSIA

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE