Empirical Bayesian Inference using Joint Sparsity

2021/03/29 by Jiahui Zhang, Zhang, Jiahui, Anne Gelb +3
Engineering · #62C12 #65C40 #68U10 #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation

paper · pdf · doi:10.48550/arxiv.2103.15618

openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across the multiple measurements in the sparse domain of the underlying signal or image, we construct a new support informed sparsity promoting prior. Several applications can be modeled using this framework, and as a prototypical example we consider reconstructing an image from synthetic aperture radar (SAR) observations using nearby azimuth angles. Our numerical experiments demonstrate that using this new prior not only improves accuracy of the recovery, but also reduces the uncertainty in the posterior when compared to standard sparsity producing priors.

Citations

• Iteratively reweighted least squares minimization for sparse recovery
• Monte Carlo sampling methods using Markov chains and their applications
• Stable signal recovery from incomplete and inaccurate measurements
• Sparsity information and regularization in the horseshoe and other shrinkage priors

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• Total Variation Bayesian Learning via Synthesis
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