Recovery Thresholding Hyperinterpolations in Signal Processing

Fuente: arXiv
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Autores principales: An, Congpei, Ran, Jiashu
Formato: Preprint
Publicado: 2025
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author An, Congpei
Ran, Jiashu
author_facet An, Congpei
Ran, Jiashu
contents This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that integrates thresholding operators--including hard thresholding, springback, and Newton thresholding--directly into the hyperinterpolation structure to maintain sparsity during signal recovery. Our approach leverages Newton's method to minimize one-dimensional nonconvex functions, which we then extend to solve multivariable nonconvex regularization problems. The proposed methods demonstrate robust performance in reconstructing signals corrupted by both Gaussian and impulse noise. Through numerical experiments, we validate the effectiveness of these recovery thresholding hyperinterpolations for signal reconstruction and function denoising applications, showing their advantages over traditional approaches in preserving signal sparsity while achieving accurate recovery.
format Preprint
id arxiv_https___arxiv_org_abs_2507_17916
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Recovery Thresholding Hyperinterpolations in Signal Processing
An, Congpei
Ran, Jiashu
Numerical Analysis
65K10, 65D15, 94A12, 65F10, 33C52
This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that integrates thresholding operators--including hard thresholding, springback, and Newton thresholding--directly into the hyperinterpolation structure to maintain sparsity during signal recovery. Our approach leverages Newton's method to minimize one-dimensional nonconvex functions, which we then extend to solve multivariable nonconvex regularization problems. The proposed methods demonstrate robust performance in reconstructing signals corrupted by both Gaussian and impulse noise. Through numerical experiments, we validate the effectiveness of these recovery thresholding hyperinterpolations for signal reconstruction and function denoising applications, showing their advantages over traditional approaches in preserving signal sparsity while achieving accurate recovery.
title Recovery Thresholding Hyperinterpolations in Signal Processing
topic Numerical Analysis
65K10, 65D15, 94A12, 65F10, 33C52
url https://arxiv.org/abs/2507.17916