Sparse Bayesian Learning Approach for Discrete Signal Reconstruction

TL;DR

This paper introduces a novel sparse Bayesian learning framework with a discretization prior for discrete signal reconstruction, significantly improving performance and computational efficiency over existing methods.

Contribution

It proposes a new discretization enforcing prior integrated into SBL and combines it with VBI and GAMP techniques for efficient, accurate discrete signal reconstruction.

Findings

The proposed methods outperform existing schemes in simulation.

GAMP-based method reduces computational burden significantly.

GAMP-based method is effective with i.i.d. Gaussian matrices but not with non-i.i.d. matrices.

Abstract

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL framework. To overcome this challenge, we introduce a novel discretization enforcing prior to exploit the knowledge of the discrete nature of the signal-of-interest. By integrating the discretization enforcing prior into the SBL framework and applying the variational Bayesian inference (VBI) methodology, we devise an alternating optimization algorithm to jointly characterize the finite-alphabet feature and reconstruct the unknown signal. When the measurement matrix is i.i.d. Gaussian per component, we further embed the generalized approximate message passing (GAMP) into the VBI-based method, so as to directly adopt the ideal prior and significantly reduce the computational burden. Simulation results demonstrate substantial performance improvement of the two proposed methods over existing schemes. Moreover, the GAMP-based variant outperforms the VBI-based method with i.i.d. Gaussian measurement matrices but it fails to work for non i.i.d. Gaussian matrices.