Quasi-sparsest solutions for quantized compressed sensing by graduated-non-convexity based reweighted ?1minimization

Abstract

In this paper, we address the problem of sparse signal recovery from scalar quantized compressed sensing measurements, via optimization. To compensate for compression losses due to dimensionality reduction and quantization, we consider a cost function that is more sparsity-inducing than the commonly used ?1-norm. Besides, we enforce a quantization consistency constraint that naturally handles the saturation issue. We investigate the potential of the recent Graduated-Non-Convexity based reweighted ?1-norm minimization for sparse recovery over polyhedral sets. We demonstrate by simulations, the robustness of the proposed approach towards saturation and its significant performance gain, in terms of reconstruction accuracy and support recovery capability.