Sparse Bayesian learning approach for discrete signal reconstruction

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 dis-cretization 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 char-acterize 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 computa-tional 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.(c) 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

This study tackles the problem of reconstructing discrete signals using sparse Bayesian learning (SBL). To overcome the challenge of using the ideal discretization prior in the SBL framework, the study introduces a novel discretization enforcing prior to leverage the knowledge of the signal's discrete nature. By integrating this prior into the SBL framework and using variational Bayesian inference (VBI), an alternating optimization algorithm is devised to characterize the feature and reconstruct the unknown signal. Simulation results demonstrate significant performance improvement of the proposed methods. The GAMP-based variant outperforms the VBI-based method with i.i.d. Gaussian measurement matrices but fails to work for non i.i.d. Gaussian matrices.