Fatma Karzan, Arkadi S. Nemirovski, Boris Polyak, Anatoli Juditsky
We discuss new methods for the recovery of signals with block-sparse structure, based on l1-minimization. Our emphasis is on the efficiently computable error bounds for the recovery routines. We optimize these bounds with respect to the method parameters to construct the estimators with improved statistical properties. We justify the proposed approach with an oracle inequality which links the properties of the recovery algorithms and the best estimation performance.