STRONGER RECOVERY GUARANTEES FOR SPARSE SIGNALS EXPLOITING COHERENCE STRUCTURE IN DICTIONARIES

This paper presents a method for improving the recovery guarantee for signals that are sparse or compressible in some general basis (dictionary) using a splitting and reordering approach. The splitting algorithm applies existing results for dictionaries that are naturally characterized as a concatenation of two sub-parts, to arbitrary dictionaries, by devising the optimal artificially induced split in the dictionary. A complete approach is presented for partitioning arbitrary dictionaries into two parts, so as to obtain the optimal coherence bounds on recovery, along with a proof of optimality. A heuristic is provided for recursive application of the splitting algorithm to further improve upon these bounds, using a multi-way dictionary split. We analyze cases where an appropriate split in the dictionary predicts less conservative signal sparsity bounds for successful recovery than those considering the dictionary as a monolithic block. Our present work does not provide a new algorithm for sparse signal recovery but rather mines for structures in the dictionary, towards strengthening the existing coherence-based recovery bounds.