通过特征矩阵进行多维非结构化稀疏恢复

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-11-19 DOI:10.1016/j.acha.2024.101725

Lexing Ying

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引用次数: 0

摘要

本说明探讨了多维非结构稀疏恢复问题。例如傅立叶反演和稀疏解卷积。特征矩阵是一种数据驱动的构造，针对一维问题提出了所需的近似特征值和特征向量。本说明将特征矩阵方法扩展到多维问题，为真实和复杂环境中的一般核和非结构化采样网格提供了相当统一的处理方法。本文提供了数值结果，以证明所提方法的性能。

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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Multidimensional unstructured sparse recovery via eigenmatrix

This note considers the multidimensional unstructured sparse recovery problems. Examples include Fourier inversion and sparse deconvolution. The eigenmatrix is a data-driven construction with desired approximate eigenvalues and eigenvectors proposed for the one-dimensional problems. This note extends the eigenmatrix approach to multidimensional problems, providing a rather unified treatment for general kernels and unstructured sampling grids in both real and complex settings. Numerical results are provided to demonstrate the performance of the proposed method.

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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.