Leveraging joint sparsity in hierarchical Bayesian learning

Jan Glaubitz; Anne Gelb

doi:10.1137/23m156255x

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arXiv · 2303.16954

Leveraging joint sparsity in hierarchical Bayesian learning

Jan Glaubitz·Anne Gelb

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Abstract

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed hyper-parameters to enforce joint sparsity. The resulting joint-sparsity-promoting priors are combined with existing Bayesian inference methods to generate a new family of algorithms. Our numerical experiments, which include a multi-coil magnetic resonance imaging application, demonstrate that our new approach consistently outperforms commonly used hierarchical Bayesian methods.

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BibTeX RIS

Jan Glaubitz, Anne Gelb. 2023-03-29. Leveraging joint sparsity in hierarchical Bayesian learning. https://doi.org/10.1137/23m156255x

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