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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.12836 |
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| _version_ | 1866911594872569856 |
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| author | Kuric, Muhamed Zach, Martin Habring, Andreas Unser, Michael Pock, Thomas |
| author_facet | Kuric, Muhamed Zach, Martin Habring, Andreas Unser, Michael Pock, Thomas |
| contents | We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent variable model, which we refer to as a Gaussian latent machine. This leads to a general sampling approach that unifies and generalizes many existing sampling algorithms in the literature. Most notably, it yields a highly efficient and effective two-block Gibbs sampling approach in the general case, while also specializing to direct sampling algorithms in particular cases. Finally, we present detailed numerical experiments that demonstrate the efficiency and effectiveness of our proposed sampling approach across a wide range of prior and posterior sampling problems from Bayesian imaging. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse Problems Kuric, Muhamed Zach, Martin Habring, Andreas Unser, Michael Pock, Thomas Image and Video Processing Computer Vision and Pattern Recognition Machine Learning 65C40, 65C05, 68U10, 65C60 We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent variable model, which we refer to as a Gaussian latent machine. This leads to a general sampling approach that unifies and generalizes many existing sampling algorithms in the literature. Most notably, it yields a highly efficient and effective two-block Gibbs sampling approach in the general case, while also specializing to direct sampling algorithms in particular cases. Finally, we present detailed numerical experiments that demonstrate the efficiency and effectiveness of our proposed sampling approach across a wide range of prior and posterior sampling problems from Bayesian imaging. |
| title | The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse Problems |
| topic | Image and Video Processing Computer Vision and Pattern Recognition Machine Learning 65C40, 65C05, 68U10, 65C60 |
| url | https://arxiv.org/abs/2505.12836 |