Denoising guarantees for optimized sampling schemes in compressed sensing
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917973504032768 |
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| author | Plan, Yaniv Scott, Matthew S. Sheng, Xia Yilmaz, Ozgur |
| author_facet | Plan, Yaniv Scott, Matthew S. Sheng, Xia Yilmaz, Ozgur |
| contents | Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind in compressed sensing, theoretical guarantees showing that the error caused by the measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming that the noise is Gaussian. We moreover provide similar guarantees for measurements sampled with-replacement with arbitrary probability weights. All our results hold on prior sets contained in a union of low-dimensional subspaces. Finally, we demonstrate that this denoising behavior appears in empirical experiments with a rate that closely matches our theoretical guarantees when the prior set is the range of a generative ReLU neural network and when it is the set of sparse vectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Denoising guarantees for optimized sampling schemes in compressed sensing Plan, Yaniv Scott, Matthew S. Sheng, Xia Yilmaz, Ozgur Machine Learning Information Theory Signal Processing Probability 94A20, 94A12, 68T07 Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind in compressed sensing, theoretical guarantees showing that the error caused by the measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming that the noise is Gaussian. We moreover provide similar guarantees for measurements sampled with-replacement with arbitrary probability weights. All our results hold on prior sets contained in a union of low-dimensional subspaces. Finally, we demonstrate that this denoising behavior appears in empirical experiments with a rate that closely matches our theoretical guarantees when the prior set is the range of a generative ReLU neural network and when it is the set of sparse vectors. |
| title | Denoising guarantees for optimized sampling schemes in compressed sensing |
| topic | Machine Learning Information Theory Signal Processing Probability 94A20, 94A12, 68T07 |
| url | https://arxiv.org/abs/2504.01046 |