Iterative Bayesian Reconstruction of Non-IID Block-Sparse Signals

TL;DR

This paper introduces a new Bayesian algorithm for reconstructing non-i.i.d. block-sparse signals using a hidden Markov model, with proven convergence and demonstrated effectiveness through experiments.

Contribution

It proposes a novel Block-IBA algorithm that models non-i.i.d. block-sparse signals with a Bernoulli-Gaussian hidden Markov model, improving reconstruction accuracy.

Findings

Proven global convergence of the Block-IBA algorithm.

Effective reconstruction demonstrated on synthetic and real data.

Outperforms existing algorithms in accuracy and robustness.

Abstract

This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identically distributed (i.i.d.), we use a more realistic Bernoulli-Gaussian hidden Markov model (BGHMM) to characterize the non-i.i.d. block-sparse signals commonly encountered in practice. The Block-IBA iteratively estimates the amplitudes and positions of the block-sparse signal using the steepest-ascent based Expectation-Maximization (EM), and optimally selects the nonzero elements of the block-sparse signal by adaptive thresholding. The global convergence of Block-IBA is analyzed and proved, and the effectiveness of Block-IBA is demonstrated by numerical experiments and simulations on synthetic and real-life data.