2021 article

A NEW HYBRID l(p)-l(2) MODEL FOR SPARSE SOLUTIONS WITH APPLICATIONS TO IMAGE PROCESSING

Gao, X., Bai, Y., Fang, S.-cherng, Luo, J., & LI, Q. (2021, December). JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION.

By: X. Gao*, Y. Bai *, S. Fang n , J. Luo * & Q. Li *

author keywords: Sparse optimization; hybrid of the l(P) quasi-norm and l(2) norm; optimality conditions; image processing
TL;DR: Computational experiments on image recovery and deblurring problems clearly confirm the superiority of the proposed model over several state-of-the-art models in terms of the signal-to-noise ratio and computational time. (via Semantic Scholar)
Source: Web Of Science
Added: December 20, 2021

<p style='text-indent:20px;'>Finding sparse solutions to a linear system has many real-world applications. In this paper, we study a new hybrid of the <inline-formula><tex-math id="M3">\begin{document}$ l_p $\end{document}</tex-math></inline-formula> quasi-norm (<inline-formula><tex-math id="M4">\begin{document}$ 0 &lt;p&lt; 1 $\end{document}</tex-math></inline-formula>) and <inline-formula><tex-math id="M5">\begin{document}$ l_2 $\end{document}</tex-math></inline-formula> norm to approximate the <inline-formula><tex-math id="M6">\begin{document}$ l_0 $\end{document}</tex-math></inline-formula> norm and propose a new model for sparse optimization. The optimality conditions of the proposed model are carefully analyzed for constructing a partial linear approximation fixed-point algorithm. A convergence proof of the algorithm is provided. Computational experiments on image recovery and deblurring problems clearly confirm the superiority of the proposed model over several state-of-the-art models in terms of the signal-to-noise ratio and computational time.</p>