A fractional coupled system for simultaneous image denoising and deblurring

Simultaneous image denoising and deblurring is a challenging issue because noise and edges are both high-frequency signals, and eliminating noise while enhancing edges counteracts each other. In this paper, we deal with this difficulty by designing a novel coupled time-fractional diffusion along with a fractional shock filter and developing a powerful discretization approach. The discretization process is based on the finite difference and L-1 approximations for integer and fractional order derivatives, respectively. This scheme not only removes noise and sharpens edges efficiently, but also weakens the staircase effect. The stability analysis of the proposed scheme is also investigated. The experimental results show that the proposed approach outperforms other related approaches and can be applied to large-scale and chest X-Ray images.