[1407.7402] Robust analysis $\ell_1$-recovery from Gaussian measurements and total variation minimization
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Computer Science > Information Theory

arXiv:1407.7402 (cs)
[Submitted on 28 Jul 2014 (v1), last revised 27 Apr 2015 (this version, v2)]

Title:Robust analysis $\ell_1$-recovery from Gaussian measurements and total variation minimization

Authors:Maryia Kabanava, Holger Rauhut, Hui Zhang
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Abstract:Analysis $\ell_1$-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.
Subjects: Information Theory (cs.IT)
Cite as: arXiv:1407.7402 [cs.IT]
  (or arXiv:1407.7402v2 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1407.7402
Journal reference: Eur. J. Appl. Math. 26 (2015) 917-929
Related DOI: https://doi.org/10.1017/S0956792515000236

Submission history

From: Maryia Kabanava [view email]
[v1] Mon, 28 Jul 2014 13:05:22 UTC (35 KB)
[v2] Mon, 27 Apr 2015 08:07:30 UTC (92 KB)
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