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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.16824 |
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| _version_ | 1866913470723653632 |
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| author | Doi, Mikiya Ohzeki, Masayuki |
| author_facet | Doi, Mikiya Ohzeki, Masayuki |
| contents | Compressed sensing is a signal processing scheme that reconstructs high-dimensional sparse signals from a limited number of observations. In recent years, various problems involving signals with a finite number of discrete values have been attracting attention in the field of compressed sensing. In particular, binary compressed sensing, which restricts signal elements to binary values $\{0, 1\}$, is the most fundamental and straightforward analysis subject in such problem settings. We evaluate the typical performance of noiseless binary compressed sensing based on $L_{1}$-norm minimization using the replica method, a statistical mechanical approach. We analyze a general setting where the elements of the observation matrix follow a Gaussian distribution, including a non-zero mean. We demonstrate that the biased observation matrix indicates more reconstruction success conditions in binary compressed sensing. Our results are consistent with the outcomes of several prior studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase transition in binary compressed sensing based on $L_{1}$-norm minimization Doi, Mikiya Ohzeki, Masayuki Statistical Mechanics Compressed sensing is a signal processing scheme that reconstructs high-dimensional sparse signals from a limited number of observations. In recent years, various problems involving signals with a finite number of discrete values have been attracting attention in the field of compressed sensing. In particular, binary compressed sensing, which restricts signal elements to binary values $\{0, 1\}$, is the most fundamental and straightforward analysis subject in such problem settings. We evaluate the typical performance of noiseless binary compressed sensing based on $L_{1}$-norm minimization using the replica method, a statistical mechanical approach. We analyze a general setting where the elements of the observation matrix follow a Gaussian distribution, including a non-zero mean. We demonstrate that the biased observation matrix indicates more reconstruction success conditions in binary compressed sensing. Our results are consistent with the outcomes of several prior studies. |
| title | Phase transition in binary compressed sensing based on $L_{1}$-norm minimization |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2405.16824 |