Line Spectral Estimation Using a G-Filter: Atomic Norm Minimization with Multiple Output Vectors
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912849389944832 |
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| author | Tang, Jiale Zhu, Bin |
| author_facet | Tang, Jiale Zhu, Bin |
| contents | We propose an atomic norm minimization (ANM) estimator of frequencies in a noisy complex sinusoidal signal that integrates Georgiou's filter bank (G-filter) with multiple output vectors (MOV). Unlike our previous work on the G-filter version of ANM which is restricted to a single filtered output vector, the proposed method in this paper uses MOV to improve data utilization and robustness of the estimate. The ANM problem with MOV can be reformulated as a semidefinite program thanks to a Carathéodory--Fejér-type decomposition for output covariance matrices of the G-filter. Numerical simulations demonstrate that the proposed approach significantly outperforms the standard ANM and the G-filter version of ANM with a single output vector in recovering the correct number of frequency components when the frequencies fall within the band(s) selected by the G-filter, particularly in the low SNR regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18279 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Line Spectral Estimation Using a G-Filter: Atomic Norm Minimization with Multiple Output Vectors Tang, Jiale Zhu, Bin Optimization and Control We propose an atomic norm minimization (ANM) estimator of frequencies in a noisy complex sinusoidal signal that integrates Georgiou's filter bank (G-filter) with multiple output vectors (MOV). Unlike our previous work on the G-filter version of ANM which is restricted to a single filtered output vector, the proposed method in this paper uses MOV to improve data utilization and robustness of the estimate. The ANM problem with MOV can be reformulated as a semidefinite program thanks to a Carathéodory--Fejér-type decomposition for output covariance matrices of the G-filter. Numerical simulations demonstrate that the proposed approach significantly outperforms the standard ANM and the G-filter version of ANM with a single output vector in recovering the correct number of frequency components when the frequencies fall within the band(s) selected by the G-filter, particularly in the low SNR regime. |
| title | Line Spectral Estimation Using a G-Filter: Atomic Norm Minimization with Multiple Output Vectors |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.18279 |