Variational Bayesian algorithm for quantized compressed sensing

TL;DR

This paper introduces a variational Bayesian algorithm for quantized compressed sensing that unifies multi-bit and 1-bit scenarios, effectively modeling quantization error as a random variable and demonstrating superior performance through extensive simulations.

Contribution

A novel variational Bayesian inference algorithm that jointly estimates signals and quantization errors, unifying multi- and 1-bit compressed sensing processing.

Findings

Outperforms state-of-the-art methods in simulations

Effective in noiseless and noisy environments

Applicable to saturated and unsaturated quantizers

Abstract

Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS algorithms. In the existing literature, the quantization error is modeled typically as additive noise and the multi-bit and 1-bit quantized CS problems are dealt with separately using different treatments and procedures. In this paper, a novel variational Bayesian inference based CS algorithm is presented, which unifies the multi- and 1-bit CS processing and is applicable to various cases of noiseless/noisy environment and unsaturated/saturated quantizer. By decoupling the quantization error from the measurement noise, the quantization error is modeled as a random variable and estimated jointly with the signal being recovered. Such a novel characterization of the quantization error results in superior performance of the algorithm which is demonstrated by extensive simulations in comparison with state-of-the-art methods for both multi-bit and 1-bit CS problems.