Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910883675897856 |
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| author | Yang, Dehui Xi, Feng |
| author_facet | Yang, Dehui Xi, Feng |
| contents | This paper is concerned with the fundamental problem of estimating chirp parameters from a mixture of linear chirp signals. Unlike most previous methods, which solve the problem by discretizing the parameter space and then estimating the chirp parameters, we propose a gridless approach by reformulating the inverse problem as a constrained two-dimensional atomic norm minimization from structured measurements. This reformulation enables the direct estimation of continuous-valued parameters without discretization, thereby resolving the issue of basis mismatch. An approximate semidefinite programming (SDP) is employed to solve the proposed convex program. Additionally, a dual polynomial is constructed to certify the optimality of the atomic decomposition. Numerical simulations demonstrate that exact recovery of chirp parameters is achievable using the proposed atomic norm minimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization Yang, Dehui Xi, Feng Signal Processing Audio and Speech Processing This paper is concerned with the fundamental problem of estimating chirp parameters from a mixture of linear chirp signals. Unlike most previous methods, which solve the problem by discretizing the parameter space and then estimating the chirp parameters, we propose a gridless approach by reformulating the inverse problem as a constrained two-dimensional atomic norm minimization from structured measurements. This reformulation enables the direct estimation of continuous-valued parameters without discretization, thereby resolving the issue of basis mismatch. An approximate semidefinite programming (SDP) is employed to solve the proposed convex program. Additionally, a dual polynomial is constructed to certify the optimality of the atomic decomposition. Numerical simulations demonstrate that exact recovery of chirp parameters is achievable using the proposed atomic norm minimization. |
| title | Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization |
| topic | Signal Processing Audio and Speech Processing |
| url | https://arxiv.org/abs/2503.15164 |