A non-convex non-smooth bi-level parameter learning for impulse and Gaussian noise mixture removing

Abstract

<p style='text-indent:20px;'>This paper introduce a novel optimization procedure to reduce mixture of Gaussian and impulse noise from images. This technique exploits a non-convex PDE-constrained characterized by a fractional-order operator. The used non-convex term facilitated the impulse component approximation controlled by a spatial parameter <inline-formula><tex-math id="M1">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula>. A non-convex and non-smooth bi-level optimization framework with a modified projected gradient algorithm is then proposed in order to learn the parameter <inline-formula><tex-math id="M2">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula>. Denoising tests confirm that the non-convex term and learned parameter <inline-formula><tex-math id="M3">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula> lead in general to an improved reconstruction when compared to results of convex norm and manual parameter <inline-formula><tex-math id="M4">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula> choice.</p>