A Multigrid Approach for Minimizing a Nonlinear Functional for Digital Image Matching

Abstract

In this paper, we consider a multigrid application in digital image processing. Here, the problem is to find a map, which transforms an image T into another image R such that the grey level of the different images are nearly equal in every picture-element. This problem arises in the investigation of human brains. The complete inverse problem is ill posed in the sense of Hadamard and nonlinear, so the numerical solution is quite difficult. We solve the inverse problem by a Landweber iteration. In each minimization step an approximate solution for the linearized problem is computed with a multigrid method as an inner iteration. Finally, we present some experimental results for synthetic and real images.