Leveraging joint sparsity in hierarchical Bayesian learning
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909209539379200 |
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| author | Glaubitz, Jan Gelb, Anne |
| author_facet | Glaubitz, Jan Gelb, Anne |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16954 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Leveraging joint sparsity in hierarchical Bayesian learning Glaubitz, Jan Gelb, Anne Machine Learning Numerical Analysis 65F22, 62F15, 65K10, 68U10 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. |
| title | Leveraging joint sparsity in hierarchical Bayesian learning |
| topic | Machine Learning Numerical Analysis 65F22, 62F15, 65K10, 68U10 |
| url | https://arxiv.org/abs/2303.16954 |