Mathematical Foundation of Sparsity-based Multi-snapshot Spectral Estimation
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866915359671451648 |
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| author | Liu, Ping Yu, Sanghyeon Sabet, Ola Pelkmans, Lucas Ammari, Habib |
| author_facet | Liu, Ping Yu, Sanghyeon Sabet, Ola Pelkmans, Lucas Ammari, Habib |
| contents | In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for sparsity-based super-resolution in such spectral estimation problems in both one- and multi-dimensional spaces. In particular, we estimate the resolution and stability of the location recovery when considering the sparsest solution under the measurement constraint, and characterize their dependence on the cut-off frequency, the noise level, the sparsity of point sources, and the incoherence of the amplitude vectors of point sources. Our estimate emphasizes the importance of the high incoherence of amplitude vectors in enhancing the resolution of multi-snapshot spectral estimation. Moreover, to the best of our knowledge, it also provides the first stability result in the super-resolution regime for the well-known sparse MMV problem in DOA estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_11189 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mathematical Foundation of Sparsity-based Multi-snapshot Spectral Estimation Liu, Ping Yu, Sanghyeon Sabet, Ola Pelkmans, Lucas Ammari, Habib Image and Video Processing Signal Processing Optics 65R32, 42A10, 62H20, 78A46 In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for sparsity-based super-resolution in such spectral estimation problems in both one- and multi-dimensional spaces. In particular, we estimate the resolution and stability of the location recovery when considering the sparsest solution under the measurement constraint, and characterize their dependence on the cut-off frequency, the noise level, the sparsity of point sources, and the incoherence of the amplitude vectors of point sources. Our estimate emphasizes the importance of the high incoherence of amplitude vectors in enhancing the resolution of multi-snapshot spectral estimation. Moreover, to the best of our knowledge, it also provides the first stability result in the super-resolution regime for the well-known sparse MMV problem in DOA estimation. |
| title | Mathematical Foundation of Sparsity-based Multi-snapshot Spectral Estimation |
| topic | Image and Video Processing Signal Processing Optics 65R32, 42A10, 62H20, 78A46 |
| url | https://arxiv.org/abs/2202.11189 |