Image Inpainting Based on Fractional-Order Nonlinear Diffusion for Image Reconstruction

Image inpainting, image deblurring, and noise removal are influential concepts in the field of digital image processing. Second-order diffusion-based image restoration models suffer from staircase effects and connectivity principle, while fourth-order models suffer from speckle artifacts. In this article, a robust image inpainting model using fractional-order nonlinear diffusion driven by difference curvature is proposed and fractional-order variational model is utilized to remove the noise and blur. Fractional-order derivatives can deal well with edges and attain good trade-off between edges preservation and elimination of staircase and speckle artifacts of an image. Difference curvature is a feature descriptor which can effectively characterize the intensity variations in the image. In this work, difference curvature-based a bi-weight, adaptive conductance coefficient is proposed to restore the image and fractional-order derivative is implemented by using discrete Fourier transform. Simulation results validate that the proposed model can adequately complete the damaged regions, solve the connectivity principle, and also avoid the staircase and speckle artifacts.