Optimized Projections for Compressed Sensing

Compressed sensing (CS) offers a joint compression and sensing processes, based on the existence of a sparse representation of the treated signal and a set of projected measurements. Work on CS thus far typically assumes that the projections are drawn at random. In this paper, we consider the optimization of these projections. Since such a direct optimization is prohibitive, we target an average measure of the mutual coherence of the effective dictionary, and demonstrate that this leads to better CS reconstruction performance. Both the basis pursuit (BP) and the orthogonal matching pursuit (OMP) are shown to benefit from the newly designed projections, with a reduction of the error rate by a factor of 10 and beyond.