A novel time-fractional decomposition model for image denoising integrating Caputo derivative

Abstract

In this work, we tackle the persistent problem of image restoration by developing a novel model that integrates a Caputo time fractional derivative into a reaction–diffusion framework. This approach exploits the memory effect of fractional derivatives for better diffusion control. With a thorough analysis employing the H^-1 norm decomposition strategy and the Weickert filter, our model excels in noise reduction and image quality preservation. The task of establishing solution existence and uniqueness was managed using the fixed point method. The results reveal substantial improvements in denoising performance, highlighting the model’s potential.