A regularized eigenmatrix method for unstructured sparse recovery

Fuente: arXiv
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Main Authors: Leem, Koung Hee, Liu, Jun, Pelekanos, George
Format: Preprint
Published: 2024
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author Leem, Koung Hee
Liu, Jun
Pelekanos, George
author_facet Leem, Koung Hee
Liu, Jun
Pelekanos, George
contents The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to numerical instability if the threshold tolerance is not appropriately chosen. To incorporate regularization techniques, we propose to regularize the eigenmatrix method by replacing the computation of an ill-conditioned pseudo-inverse by the solution of an ill-conditioned least square system, which can be efficiently treated by Tikhonov regularization. Extensive numerical examples confirmed the improved effectiveness of our proposed method, especially when the noise levels are relatively high.
format Preprint
id arxiv_https___arxiv_org_abs_2405_08721
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A regularized eigenmatrix method for unstructured sparse recovery
Leem, Koung Hee
Liu, Jun
Pelekanos, George
Numerical Analysis
65R32, 65F22
The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to numerical instability if the threshold tolerance is not appropriately chosen. To incorporate regularization techniques, we propose to regularize the eigenmatrix method by replacing the computation of an ill-conditioned pseudo-inverse by the solution of an ill-conditioned least square system, which can be efficiently treated by Tikhonov regularization. Extensive numerical examples confirmed the improved effectiveness of our proposed method, especially when the noise levels are relatively high.
title A regularized eigenmatrix method for unstructured sparse recovery
topic Numerical Analysis
65R32, 65F22
url https://arxiv.org/abs/2405.08721