Robust analysis ${\ell }_1$-recovery from Gaussian measurements and total variation minimization

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.

References in corpus (3)

• Greedy-Like Algorithms for the Cosparse Analysis Model
• Near-optimal compressed sensing guarantees for total variation minimization
• Corrupted Sensing: Novel Guarantees for Separating Structured Signals

Cited by in corpus (6)

• ${\ell }^1$-Analysis Minimization and Generalized (Co-)Sparsity: When Does Recovery Succeed?
• One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations
• Compressed Sensing with 1D Total Variation: Breaking Sample Complexity Barriers via Non-Uniform Recovery
• Living near the edge: A lower-bound on the phase transition of total variation minimization
• Sample Complexity of Total Variation Minimization
• Generalization analysis of an unfolding network for analysis-based Compressed Sensing