OMP with Highly Coherent Dictionaries

Recovering signals that has a sparse representation from a given set of linear measurements has been a major topic of research in recent years. Most of the work dealing with this subject focus on the reconstruction of the signal’s representation as the means to recover the signal itself. This approach forces the dictionary to be of low-coherence and with no linear dependencies between its columns. Recently, a series of contributions show that such dependencies can be allowed by aiming at recovering the signal itself. However, most of these recent works consider the analysis framework, and only few discuss the synthesis model. This paper studies the synthesis and introduces a new mutual coherence definition for signal recovery, showing that a modified version of OMP can recover sparsely represented signals of a dictionary with very high correlations between pairs of columns. We show how the derived results apply to the plain OMP.