A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise

Multiplicative noise removal from texture images poses a significant challenge. Different from the diffusion equation-based filter, we consider the telegraph diffusion equation-based model, which can effectively preserve fine structures and edges for texture images. The fractional-order derivative is imposed due to its textural detail enhancing capability. We also introduce the gray level indicator, which fully considers the gray level information of multiplicative noise images, so that the model can effectively remove high level noise and protect the details of the structure. The well-posedness of the proposed fractional-order telegraph diffusion model is presented by applying the Schauder's fixed-point theorem. To solve the model, we develop an iterative algorithm based on the discrete Fourier transform in the frequency domain. We give various numerical results on despeckling natural and real SAR images. The experiments demonstrate that the proposed method can remove multiplicative noise and preserve texture well.