A Proximal–Based Algorithm for Piecewise Sparse Approximation with Application to Scattered Data Fitting

In some applications, there are signals with a piecewise structure to be recovered. In this paper, we propose a piecewise sparse approximation model and a piecewise proximal gradient method (JPGA) which aim to approximate piecewise signals. We also make an analysis of the JPGA based on differential...

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Bibliographic Details
Published in:International journal of applied mathematics and computer science Vol. 32; no. 4; pp. 671 - 682
Main Authors: Zhong, Yijun, Li, Chongjun, Li, Zhong, Duan, Xiaojuan
Format: Journal Article
Language:English
Published: Zielona Góra Sciendo 01.12.2022
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:
Algorithms
Approximation
Differential equations
Mathematical analysis
Phase transitions
piecewise sparse approximation
proximal gradient
Representations
scattered data fitting
Signal processing
Sparsity
ISSN:1641-876X, 2083-8492
Online Access:Get full text
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Summary:In some applications, there are signals with a piecewise structure to be recovered. In this paper, we propose a piecewise sparse approximation model and a piecewise proximal gradient method (JPGA) which aim to approximate piecewise signals. We also make an analysis of the JPGA based on differential equations, which provides another perspective on the convergence rate of the JPGA. In addition, we show that the problem of sparse representation of the fitting surface to the given scattered data can be considered as a piecewise sparse approximation. Numerical experimental results show that the JPGA can not only effectively fit the surface, but also protect the piecewise sparsity of the representation coefficient.
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ISSN:1641-876X
2083-8492
DOI:10.34768/amcs-2022-0046