Robust group lasso: Model and recoverability

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 high probability for a very general class of A(i)'s.