Frame-based block sparse compressed sensing via l2/l1-synthesis

Abstract In this paper we consider the frame-based block sparse signal recovery via a l2/l1-synthesis method. A new kind of null space property based on the given dictionary D(block D-NSP) is proposed. It is proved that sensing matrices satisfying the block D-NSP is not just a sufficient and necessary condition for the l2/l1-synthesis method to exactly recover signals that are block sparse in frame D, but also a sufficient and necessary condition for the l2/l1-synthesis to stably recover signals which are block-compressible in frame D. To the best of our knowledge, this new property is the first sufficient and necessary condition for successful signal recovery via the l2/l1-synthesis. In addition, we also characterize the theoretical performance of recovering signals via the l2/l1-synthesis in the case of the measurements are disturbed. Mathematics Subject Classification: 94A12,94A15