Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization

Dehui Yang; Feng Xi

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arXiv · 2503.15164

Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization

Dehui Yang·Feng Xi

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Abstract

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.

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BibTeX RIS

Dehui Yang, Feng Xi. 2025-03-19. Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization. https://arxiv.org/abs/2503.15164

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