基于特征矩阵的未知噪声下的稀疏自由反卷积

IF 3.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2025-08-14 DOI:10.1016/j.acha.2025.101802

Lexing Ying

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引用次数: 0

摘要

本文研究未知噪声水平下稀疏谱测度的谱估计问题。求解非结构化稀疏恢复问题的主要技术工具是特征矩阵法。当噪声水平确定后，自由反褶积将问题简化为可应用特征矩阵方法的非结构化稀疏恢复问题。为了确定未知噪声水平，我们提出了一个基于特征矩阵法中间矩阵奇异值的优化问题。给出了加性和乘性自由反卷积的数值结果。

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Sparse free deconvolution under unknown noise level via eigenmatrix

This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is determined, the free deconvolution reduces the problem to an unstructured sparse recovery problem to which the eigenmatrix method can be applied. To determine the unknown noise level, we propose an optimization problem based on the singular values of an intermediate matrix of the eigenmatrix method. Numerical results are provided for both the additive and multiplicative free deconvolutions.

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.