Sparse Bayesian Learning Approach for Discrete Signal Reconstruction
It addresses signal reconstruction for discrete signals, which is incremental as it builds on existing sparse Bayesian learning methods.
This study tackled the problem of discrete signal reconstruction by introducing a novel discretization enforcing prior within the sparse Bayesian learning framework, resulting in substantial performance improvements over existing schemes, with the GAMP-based variant outperforming the VBI-based method for i.i.d. Gaussian matrices.
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.