Algorithms to Approximately Solve NP Hard Row-Sparse MMV Recovery Problem: Application to Compressive Color Imaging

Abstract

This paper addresses the row-sparse multiple measurement vector (MMV) recovery problem. This requires solving a nondeterministic polynomial (NP) hard optimization. Instead of approximating the NP hard problem by its convex/nonconvex surrogates as is done in other studies, we propose techniques to directly solve the NP hard problem approximately with tractable algorithms. The algorithms derived in here yields better recovery rates than the state-of-the-art convex (spectral projected gradient) algorithm we compared against. We show that the compressive color image reconstruction can be formulated as an MMV recovery problem with sparse rows and therefore can be solved by our proposed method. The reconstructed images are more accurate (improvement about 2 dB in peak signal-to-noise ratio) than the previous technique compared against.