Fractional nonlinear anisotropic diffusion with p-Laplace variation method for image restoration

Abstract

In this paper, a novel class of fractional-order nonlinear anisotropic diffusion equations based image restoration model is established, which employs the p-Laplace norm of fractional-order gradient of an image intensity function. The role of the fractional-order gradient is to better accommodate the texture details of an image, and the adaptive factor p can be used to diffuse adaptively according to local geometry features, which are fractional-order curvature and fractional-order gradient of an image. Besides removing noise and non-linearly keeping high-frequency edge of images efficiently, our proposed model can enhance the texture details of images and greatly eliminate the staircase effects and also the speckle effects. Fourier transform technique is also proposed to compute the fractional order derivative. Experimental results illustrate that our proposed model can deal with edge preserving and texture enhancing, more efficiently than the other four methods and outperform the other four methods by means of PSNR. Our average PSNR is closed to 1dB higher than the average PSNRs of the other four methods.