Total fractional-order variation and bilateral filter for image denoising

Image denoising stands out as a primary goal in image processing.  However, many existing methods encounter challenges in preserving features such as corners and edges of an image while deleting the noise.  This study investigates and evaluates a fractional-order derivative based on the total $\alpha$-order variation (TV) model and the bilateral total variation (BTV) model.  This choice is motivated by the proven effectiveness of the TV model in noise removal and edge preservation, with the BTV model further utilized to enhance the restoration of fine and intricate details.  The experimental results affirm the efficacy of the proposed model, supported by objective quantitative metrics and subjective assessments of visual appearance.