A non-convex denoising model for impulse and Gaussian noise mixture removing using bi-level parameter identification

<p style='text-indent:20px;'>We propose a new variational framework to remove mixture of Gaussian and impulse noise from images. This is based on non-convex PDE-constrained with fractional-order operator. The norm applied the component controlled by weighted parameter <inline-formula><tex-math id="M1">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula>, which depends level image feature. Furthermore, fractional operator used preserve texture edges. In first part, we study theoretical properties proposed PDE-constrained, show some well-posdnees results. second after having demonstrated how numerically find minimizer, proximal linearized algorithm combined Primal-Dual approach introduced. Moreover, bi-level optimization projected gradient in order automatically select id="M2">\begin{document}$ $\end{document}</tex-math></inline-formula>. Denoising tests confirm that term learned id="M3">\begin{document}$ $\end{document}</tex-math></inline-formula> lead general an improved reconstruction when compared results convex other competitive denoising methods. Finally, extensive experiments various images intensities report conventional numerical validity its analysis also learning data.</p>