A Non-Convex Fractional-Order Differential Equation for Medical Image Restoration

We propose a new non-convex fractional-order Weber multiplicative denoising variational generalized function, which leads to a new fractional-order differential equation, and prove the existence of a unique solution to this equation. Furthermore, the model is solved using the partial differential equation (PDE) method and the alternating direction multiplier method (ADMM) to verify the theoretical results. The proposed model is tested on some symmetric and asymmetric medical computerized tomography (CT) images, and the experimental results show that the combination of the fractional-order differential equation and the Weber function has better performance in medical image restoration than the traditional model.