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This paper considers the problem of recovering a group sparse signal matrix$\mathbf{Y} = [\mathbf{y}_1, \cdots, \mathbf{y}_L]$ from sparsely corruptedmeasurements $\mathbf{M} = [\mathbf{A}_{(1)}\mathbf{y}_{1}, \cdots,\mathbf{A}_{(L)}\mathbf{y}_{L}] + \mathbf{S}$, where $\mathbf{A}_{(i)}$'s areknown sensing matrices and $\mathbf{S}$ is an unknown sparse error matrix. Arobust group lasso (RGL) model is proposed to recover $\mathbf{Y}$ and$\mathbf{S}$ through simultaneously minimizing the $\ell_{2,1}$-norm of$\mathbf{Y}$ and the $\ell_1$-norm of $\mathbf{S}$ under the measurementconstraints. We prove that $\mathbf{Y}$ and $\mathbf{S}$ can be exactlyrecovered from the RGL model with a high probability for a very general classof $\mathbf{A}_{(i)}$'s.

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