Analysis of iterative methods for solving a Ginzburg-Landau equation

Abstract. Very recently we have proposed to use a complex Ginzburg-Landau equation for high contrast inpainting, to restore higher dimensional (volumetric) data (which has applications in frame interpolation), improving sparsely sampled data and to fill in fragmentary surfaces. In this paper we review digital inpainting algorithms and compare their performance with a Ginzburg-Landau inpainting model. For the solution of the Ginzburg-Landau equation we compare the performance of several numerical algorithms. A stability and convergence analysis is given and the consequences for applications to digital inpainting are discussed. Keywords: Ginzburg-Landau equation, inpainting, diffusion filtering, non-linear partial differential equations, variational problems AMS: 35K57, 65M06