Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization
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.
Cite
@article{arxiv.2503.15164,
title = {Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization},
author = {Dehui Yang and Feng Xi},
journal= {arXiv preprint arXiv:2503.15164},
year = {2025}
}