Eigenmatrix for unstructured sparse recovery

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-03-14 DOI:10.1016/j.acha.2024.101653

Lexing Ying

引用次数: 0

Abstract

This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are the noise in the sample values and the unstructured nature of the sample locations. This note proposes the eigenmatrix, a data-driven construction with desired approximate eigenvalues and eigenvectors. The eigenmatrix offers a new way for these sparse recovery problems. Numerical results are provided to demonstrate the efficiency of the proposed method.

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非结构稀疏恢复的特征矩阵

本说明考虑了一般形式的非结构稀疏恢复问题。例子包括有理近似、频谱函数估计、傅立叶反演、拉普拉斯反演和稀疏解卷积。主要挑战在于样本值的噪声和样本位置的非结构性。本说明提出了特征矩阵，这是一种数据驱动的结构，具有所需的近似特征值和特征向量。特征矩阵为这些稀疏恢复问题提供了一种新的方法。本文提供了数值结果，以证明所提方法的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.