Vol. 1, No. 1, 2013

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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
TV-min and greedy pursuit for constrained joint sparsity and application to inverse scattering

Albert Fannjiang

Vol. 1 (2013), No. 1, 81–104
Abstract

This paper proposes a general framework for compressed sensing of constrained joint sparsity (CJS) which includes total variation minimization (TV-min) as an example. The gradient- and 2-norm error bounds, independent of the ambient dimension, are derived for the CJS version of basis pursuit and orthogonal matching pursuit. As an application the results extend Candès, Romberg, and Tao’s proof of exact recovery of piecewise constant objects with noiseless incomplete Fourier data to the case of noisy data.

Keywords
total variation, joint sparsity, multiple measurement vectors, compressive sensing
Mathematical Subject Classification 2010
Primary: 15A29
Milestones
Received: 11 May 2012
Revised: 17 September 2012
Accepted: 12 November 2012
Published: 6 February 2013

Communicated by Micol Amar
Authors
Albert Fannjiang
Department of Mathematics
University of California, Davis
One Shields Ave.
Davis, CA 95616-8633
United States