Open AccessSmoothing Newton method for $ \ell^0 $-$ \ell^2 $ regularized linear inverse problem
Author(s) -
Peili Li,
Xiliang Lu,
Yunhai Xiao
Publication year - 2022
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021044
Subject(s) - smoothing , mathematics , regularization (linguistics) , inverse , inverse problem , convergence (economics) , algorithm , combinatorics , computer science , mathematical analysis , artificial intelligence , geometry , statistics , economics , economic growth
Sparse regression plays a very important role in statistics, machine learning, image and signal processing. In this paper, we consider a high-dimensional linear inverse problem with \begin{document}$ \ell^0 $\end{document} - \begin{document}$ \ell^2 $\end{document} penalty to stably reconstruct the sparse signals. Based on the sufficient and necessary condition of the coordinate-wise minimizers, we design a smoothing Newton method with continuation strategy on the regularization parameter. We prove the global convergence of the proposed algorithm. Several numerical examples are provided, and the comparisons with the state-of-the-art algorithms verify the effectiveness and superiority of the proposed method.