Identifiability for Gauge Regularizations and Algorithms for Block-Sparse Synthesis in Compressive Sensing

In the paper we give a characterization of identifiability for regularizations with gauges of compact convexes. This extends the classic identifiability results from the standard l1-regularization framework in compressive sensing. We show that the standard dual certificate techniques can no longer work by themselves ouside the polytope case. We then apply the general characterization to the caseof block-sparse regularizations and obtain an identification algorithm based on a combination of the standard duality and a convex-projection technique.