A Novel Fractional-Order Variational Approach for Image Restoration Based on Fuzzy Membership Degrees

We propose a new fractional-order (space and time) total variation regularized model for multiplicative noise removal in this research article. We use the regularly varying fuzzy membership degrees to characterize the likelihood of a pixel related to edges, texture regions, and flat regions to improve model efficiency. This approach is capable of maintaining edges, textures, and other image information while significantly reducing the blocky effect. We opt for the option of local actions. In order to efficiently find the minimizer of the prescribed energy function, the semi-implicit gradient descent approach is used (which derives the corresponding fractional-order Euler-Lagrange equations). The existence and uniqueness of a solution to the suggested variational model are proved. Experimental results show the efficiency of the suggested model in visual enhancement, preserving details and reducing the blocky effect while extracting noise as well as an increase in the PSNR (dB), SSIM, relative error, and less CPU time(s) comparing to other schemes.