Approximate Message Passing with Parameter Estimation for Heavily Quantized Measurements

TL;DR

This paper introduces a novel AMP-based framework for joint signal and parameter estimation in heavily quantized noisy measurements, improving sparse recovery performance in applications like radar and wireless sensing.

Contribution

It presents a new AMP-based method that estimates unknown parameters as posteriors, enabling joint recovery of signals and parameters, including for 1-bit and multi-bit quantization models.

Findings

Significant performance improvements over state-of-the-art methods.

Effective handling of 1-bit and multi-bit quantization noise models.

Robust recovery across various sparsity and noise levels.

Abstract

Designing efficient sparse recovery algorithms that could handle noisy quantized measurements is important in a variety of applications -- from radar to source localization, spectrum sensing and wireless networking. We take advantage of the approximate message passing (AMP) framework to achieve this goal given its high computational efficiency and state-of-the-art performance. In AMP, the signal of interest is assumed to follow certain prior distribution with unknown parameters. Previous works focused on finding the parameters that maximize the measurement likelihood via expectation maximization -- an increasingly difficult problem to solve in cases involving complicated probability models. In this paper, we treat the parameters as unknown variables and compute their posteriors via AMP. The parameters and signal of interest can then be jointly recovered. Compared to previous methods, the proposed approach leads to a simple and elegant parameter estimation scheme, allowing us to directly work with 1-bit quantization noise model. We then further extend our approach to general multi-bit quantization noise model. Experimental results show that the proposed framework provides significant improvement over state-of-the-art methods across a wide range of sparsity and noise levels.