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Paper details
Number 4 - December 2022
Volume 32 - 2022
A proximal-based algorithm for piecewise sparse approximation with application to scattered data fitting
Yijun Zhong, Chongjun Li, Zhong Li, Xiaojuan Duan
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.
Keywords
piecewise sparse approximation, proximal gradient, scattered data fitting