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arXiv · 1407.7402

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

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.

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Maryia Kabanava, Holger Rauhut, Hui Zhang. 2015-04-27. Robust analysis $\ell_1$-recovery from Gaussian measurements and total variation minimization. https://doi.org/10.1017/s0956792515000236

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