Plug-And-Play Learned Gaussian-mixture Approximate Message Passing

TL;DR

This paper introduces L-GM-AMP, a plug-and-play compressed sensing recovery algorithm that uses a learned Gaussian-mixture denoiser, achieving state-of-the-art results without prior source knowledge.

Contribution

It presents a universal, learned denoising function based on Gaussian mixtures within AMP, improving robustness and performance over previous methods.

Findings

Achieves state-of-the-art performance in compressed sensing recovery.

Robustly handles mixture and discrete source distributions.

Does not require prior knowledge of the source distribution.

Abstract

Deep unfolding showed to be a very successful approach for accelerating and tuning classical signal processing algorithms. In this paper, we propose learned Gaussian-mixture AMP (L-GM-AMP) - a plug-and-play compressed sensing (CS) recovery algorithm suitable for any i.i.d. source prior. Our algorithm builds upon Borgerding's learned AMP (LAMP), yet significantly improves it by adopting a universal denoising function within the algorithm. The robust and flexible denoiser is a byproduct of modelling source prior with a Gaussian-mixture (GM), which can well approximate continuous, discrete, as well as mixture distributions. Its parameters are learned using standard backpropagation algorithm. To demonstrate robustness of the proposed algorithm, we conduct Monte-Carlo (MC) simulations for both mixture and discrete distributions. Numerical evaluation shows that the L-GM-AMP algorithm achieves state-of-the-art performance without any knowledge of the source prior.