A fractional differential fidelity-based PDE model for image denoising

Abstract

In this paper, a new partial differential equation (PDE)-based model is proposed for image denoising. The new method is inspired by previous works in which the nonlinear diffusion approach obtained by using a coupling gradient fidelity term. Based on the long-term memory and nonlocality of fractional differential, we introduce a new fidelity term based on the combination of fractional-order fidelity term and global fidelity term to measure the similarity in the variation of images, which can prevent the staircase effect, and simultaneously enhance the noisy image, thus, the image becomes clearer and brighter. Numerical results are presented in the end to demonstrate that with respect to image denoising capability, our fractional fidelity-based model outperforms the gradient fidelity-based model.

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