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

Fuente: arXiv
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Main Authors: Yang, Dehui, Xi, Feng
Format: Preprint
Published: 2025
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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