Bayesian Sparse Blind Deconvolution Using MCMC Methods Based on Normal-Inverse-Gamma Prior

TL;DR

This paper introduces a new MCMC-based Bayesian approach for sparse blind deconvolution using a Normal-Inverse-Gamma prior, which improves computational efficiency over traditional Bernoulli-Gaussian models by avoiding discrete sampling issues.

Contribution

The paper proposes a continuous-valued NIG prior for sparse sequences in blind deconvolution, enabling more efficient Gibbs sampling and overcoming computational bottlenecks of BG models.

Findings

Significant reduction in computational time compared to BG-based methods

Effective incorporation of time and frequency domain constraints

Validated through extensive simulations showing improved performance

Abstract

Bayesian estimation methods for sparse blind deconvolution problems conventionally employ Bernoulli-Gaussian (BG) prior for modeling sparse sequences and utilize Markov Chain Monte Carlo (MCMC) methods for the estimation of unknowns. However, the discrete nature of the BG model creates computational bottlenecks, preventing efficient exploration of the probability space even with the recently proposed enhanced sampler schemes. To address this issue, we propose an alternative MCMC method by modeling the sparse sequences using the Normal-Inverse-Gamma (NIG) prior. We derive effective Gibbs samplers for this prior and illustrate that the computational burden associated with the BG model can be eliminated by transferring the problem into a completely continuous-valued framework. In addition to sparsity, we also incorporate time and frequency domain constraints on the convolving sequences. We demonstrate the effectiveness of the proposed methods via extensive simulations and characterize computational gains relative to the existing methods that utilize BG modeling.