Recoverability of Group Sparse Signals from Corrupted Measurements via Robust Group Lasso

2015/09/28 by Xiaohan Wei, Qing Ling, Wei, Xiaohan +3
Computer Science · Engineering · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1509.08490

openalex publication_date 2015/09/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper considers the problem of recovering a group sparse signal matrix Y = [y₁, ⋯, y_L] from sparsely corrupted measurements M = [A₍₁₎y₁, ⋯, A_(L)y_L] + S, where A_(i)'s are known sensing matrices and S is an unknown sparse error matrix. A robust group lasso (RGL) model is proposed to recover Y and S through simultaneously minimizing the ℓ_2,1-norm of Y and the ℓ₁-norm of S under the measurement constraints. We prove that Y and S can be exactly recovered from the RGL model with a high probability for a very general class of A_(i)'s.

Citations

• Robust principal component analysis?

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