Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.09483 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916480111607808 |
|---|---|
| author | Böck, Benedikt Syed, Sadaf Utschick, Wolfgang |
| author_facet | Böck, Benedikt Syed, Sadaf Utschick, Wolfgang |
| contents | This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular, sparse Bayesian learning (SBL), to integrate a strong regularization towards sparse solutions. At the same time, by leveraging the notion of conditional Gaussianity, it also incorporates the adaptability from generative models to training data. However, unlike most state-of-the-art generative models, it is able to learn from a few compressed and noisy data samples and requires no optimization algorithm for solving the inverse problem. Additionally, similar to Dirichlet prior networks, our model parameterizes a conjugate prior enabling its application for uncertainty quantification. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse Bayesian Generative Modeling for Compressive Sensing Böck, Benedikt Syed, Sadaf Utschick, Wolfgang Machine Learning Image and Video Processing This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular, sparse Bayesian learning (SBL), to integrate a strong regularization towards sparse solutions. At the same time, by leveraging the notion of conditional Gaussianity, it also incorporates the adaptability from generative models to training data. However, unlike most state-of-the-art generative models, it is able to learn from a few compressed and noisy data samples and requires no optimization algorithm for solving the inverse problem. Additionally, similar to Dirichlet prior networks, our model parameterizes a conjugate prior enabling its application for uncertainty quantification. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals. |
| title | Sparse Bayesian Generative Modeling for Compressive Sensing |
| topic | Machine Learning Image and Video Processing |
| url | https://arxiv.org/abs/2411.09483 |