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

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Big Data and Artificial Intelligence for Cooperative Vehicle-Infrastructure Systems (Special section, pp. 523-599), Baozhen Yao, Shuaian (Hans) Wang and Sobhan (Sean) Asian (Eds.)


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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Mathematik, Angewandte Mathematik