Block sparse recovery via mixed l 2/l 1 minimization

We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ ₂ s < 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l ₂/l ₁-minimization approach in the noiseless case and is stably recovered in the presence of noise and mismodeling error. This improves the result of Eldar and Mishali (in IEEE Trans. Inform. Theory 55: 5302–5316, 2009). We also give another sufficient condition on block RIP for such recovery method: δ _s < 0.307.