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