A Learning-Based Framework for Quantized Compressed Sensing

Abstract

Sparse recovery from undersampled random quantization measurements is a recent active research topic. Previous work asserts that stable recovery can be guaranteed via the basis pursuit dequantizer (BPDQ) if the measurements number is large enough, considering random sampling patterns. In this letter, we study a learning-based method for optimizing the sampling pattern, within the framework of sparse recovery via BPDQ from their uniformly quantized measurements. Given a set of representative training signals, the method finds the sampling pattern that performs the best on average over these signals. We compare our approach with the random sampling and other state-of-the-art sampling methods, which shows that it achieves superior reconstruction performance. We demonstrate that proper accounting for sampling and careful sampler design has a significant impact on the performance of quantized compressive sensing methods.