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

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 \begin{document}$ \gamma $\end{document} . A non-convex and non-smooth bi-level optimization framework with a modified projected gradient algorithm is then proposed in order to learn the parameter \begin{document}$ \gamma $\end{document} . Denoising tests confirm that the non-convex term and learned parameter \begin{document}$ \gamma $\end{document} lead in general to an improved reconstruction when compared to results of convex norm and manual parameter \begin{document}$ \lambda $\end{document} choice.