Soft Recovery Through ℓ_1,2 Minimization with Applications in Recovery of Simultaneously Sparse and Low-Rank Matrice

2016/09/08 by Axel Flinth, Flinth, Axel
Computer Science · Engineering · #52A41 #90C25 #Blind Source Separation Techniques #Electrical and Bioimpedance Tomography #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1609.02302

openalex publication_date 2016/09/08 · openalex created_date 2016/09/23 · openalex updated_date 2026/07/28

Abstract

This article provides a new type of analysis of a compressed-sensing based technique for recovering column-sparse matrices, namely minimization of the ℓ_1,2-norm. Rather than providing conditions on the measurement matrix which guarantees the solution of the program to be exactly equal to the ground truth signal (which already has been thoroughly investigated), it presents a condition which guarantees that the solution is approximately equal to the ground truth. Soft recovery statements of this kind are to the best knowledge of the author a novelty in Compressed Sensing. Apart from the theoretical analysis, we present two heuristic proposes how this property of the ℓ_1,2-program can be utilized to design algorithms for recovery of matrices which are sparse and have low rank at the same time.

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