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

This paper considers the problem of recovering a group sparse signal matrix Y = [y1, · · · ,yL] from sparsely corrupted measurements M = [A(1)y1, · · · ,A(L)yL] + 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 l2,1-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.