  This paper considers the problem of recovering a group sparse signal matrix
$\mathbf{Y} = [\mathbf{y}_1, \cdots, \mathbf{y}_L]$ from sparsely corrupted
measurements $\mathbf{M} = [\mathbf{A}_{(1)}\mathbf{y}_{1}, \cdots,
\mathbf{A}_{(L)}\mathbf{y}_{L}] + \mathbf{S}$, where $\mathbf{A}_{(i)}$'s are
known sensing matrices and $\mathbf{S}$ is an unknown sparse error matrix. A
robust 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 measurement
constraints. We prove that $\mathbf{Y}$ and $\mathbf{S}$ can be exactly
recovered from the RGL model with a high probability for a very general class
of $\mathbf{A}_{(i)}$'s.
