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Robust analysis ℓ1-recovery from Gaussian measurements and total variation minimization†

Published online by Cambridge University Press:  01 June 2015

M. KABANAVA ,
H. RAUHUT  and
H. ZHANG
M. KABANAVA
Affiliation:
Chair for Mathematics C (Analysis), RWTH Aachen University, Templegraben 55, 52062 Aachen, Germany email: kabanava@mathc.rwth-aachen.de; rauhut@mathc.rwth-aachen.de
H. RAUHUT
Affiliation:
Chair for Mathematics C (Analysis), RWTH Aachen University, Templegraben 55, 52062 Aachen, Germany email: kabanava@mathc.rwth-aachen.de; rauhut@mathc.rwth-aachen.de
H. ZHANG
Affiliation:
College of Science, National University of Defense Technology, Changsha, Hunan, 410073China email: hhuuii.zhang@gmail.com
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Abstract

Analysis ℓ1-recovery refers to a technique of recovering a signal that is sparse in some transform domain from incomplete corrupted measurements. This includes total variation minimization as an important special case when the transform domain is generated by a difference operator. In the present paper, we provide a bound on the number of Gaussian measurements required for successful recovery for total variation and for the case that the analysis operator is a frame. The bounds are particularly suitable when the sparsity of the analysis representation of the signal is not very small.

Keywords

compressive sensingℓ1-minimizationTV-normframesGaussian random matrices
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 6 , December 2015 , pp. 917 - 929
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

†

M. Kabanava and H. Rauhut acknowledge support by the European Research Council through the grant StG 258926. H. Zhang is supported by China NSF Grants No. 61201328.

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