Expectation-Maximization-Aided Hybrid Generalized Expectation Consistent for Sparse Signal Reconstruction

TL;DR

This paper introduces EM-aided HyGEC, an algorithm for sparse signal reconstruction with non-i.i.d. group priors, addressing stability and hyper-parameter estimation issues through an EM framework combined with a GEC-based inner engine.

Contribution

It proposes a novel EM-aided HyGEC algorithm that improves stability and hyper-parameter learning in sparse signal reconstruction with group-structured priors.

Findings

The algorithm effectively stabilizes reconstruction in ill-conditioned scenarios.

It accurately learns hyper-parameters without prior knowledge.

Numerical simulations confirm its superior performance.

Abstract

The reconstruction of sparse signal is an active area of research. Different from a typical i.i.d. assumption, this paper considers a non-independent prior of group structure. For this more practical setup, we propose EM-aided HyGEC, a new algorithm to address the stability issue and the hyper-parameter issue facing the other algorithms. The instability problem results from the ill condition of the transform matrix, while the unavailability of the hyper-parameters is a ground truth that their values are not known beforehand. The proposed algorithm is built on the paradigm of HyGAMP (proposed by Rangan et al.) but we replace its inner engine, the GAMP, by a matrix-insensitive alternative, the GEC, so that the first issue is solved. For the second issue, we take expectation-maximization as an outer loop, and together with the inner engine HyGEC, we learn the value of the hyper-parameters. Effectiveness of the proposed algorithm is also verified by means of numerical simulations.