A novel weighted fractional order variable exponent total variation model and its algorithm

A novel weighted total variation model incorporating a fractional order variable exponent is proposed, designed to achieve adaptive smoothing in key image regions while effectively preserving edge information. Based on the properties of the log-exp function, an adaptive weighting function is introduced, assigning lower weights to edges and higher weights to smooth areas, thus enhancing structural detail retention and noise suppression. Through variational analysis, the corresponding Euler–Lagrange equation is derived, transforming the optimization problem into a gradient descent flow formulation amenable to efficient numerical solution. Extensive comparative experiments on three benchmark datasets demonstrate that the proposed approach yields substantial improvements over baseline methods and achieves performance competitive with state-of-the-art models.