Multi-Modal Potential Based Non-linear PDE Model for Grayscale Image Inpainting

Abstract In this paper, we propose a multi-well potential based modified Cahn-Hilliardmodel for gray-scale image inpainting. An image specific multi-well potentialfunction is constructed from the histogram information of the given image. Existence,uniqueness and the continuous dependency of the solution on the initialdata, of the newly proposed modified Cahn-Hilliard equation has been establishedusing Faedo-Galerkin approach. Also the complete discretization error forthe numerical scheme based on convexity splitting in time and Fourier spectralmethod in space has been derived. Numerical simulations have been carried outon some standard gray-scale test images and the metrics PSNR, SNR, SSIMcorresponding to the obtained results are compared with those in the literature.