Eigenmatrix for unstructured sparse recovery
Numerical Analysis
2024-03-11 v4 Information Theory
Machine Learning
Numerical Analysis
Signal Processing
math.IT
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.
Cite
@article{arxiv.2311.16609,
title = {Eigenmatrix for unstructured sparse recovery},
author = {Lexing Ying},
journal= {arXiv preprint arXiv:2311.16609},
year = {2024}
}