<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

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

Published Online: Dec 30, 2022

Page range: 671 - 682

Received: Dec 16, 2021

Accepted: Jun 13, 2022

DOI: https://doi.org/10.34768/amcs-2022-0046

Keywords
piecewise sparse approximation, proximal gradient, scattered data fitting

© 2022 Yijun Zhong et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Dec 30, 2022

Page range: 671 - 682

Received: Dec 16, 2021

Accepted: Jun 13, 2022

DOI: https://doi.org/10.34768/amcs-2022-0046

Keywordspiecewise sparse approximation, proximal gradient, scattered data fitting

© 2022 Yijun Zhong et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
piecewise sparse approximation, proximal gradient, scattered data fitting