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

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.

arXiv comment15 pages, 4 figures. This paper has been submitted to IEEE Signal Processing Letters

References in corpus (6)

• Massive Connectivity with Massive MIMO-Part I: Device Activity Detection and Channel Estimation
• Expectation-Maximization Gaussian-Mixture Approximate Message Passing
• Bayes-Optimal Joint Channel-and-Data Estimation for Massive MIMO with Low-Precision ADCs
• Compressive Imaging using Approximate Message Passing and a Markov-Tree Prior
• Hybrid Approximate Message Passing
• Plug-in Estimation in High-Dimensional Linear Inverse Problems: A Rigorous Analysis