A multigrid method for anisotropic PDEs in elastic image registration

✍ Scribed by Lars Hömke

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 390 KB
• Volume: 13
• Category: Article
• ISSN: 1070-5325
• DOI: 10.1002/nla.477

✦ Synopsis

Abstract

This paper deals with the solution of a non‐linear ill‐conditioned inverse problem arising in digital image registration. In the first part of the paper, we define the problem as the minimization of a regularized non‐linear least‐squares functional, which measures the image difference and smoothness of the transformation. We study inexact Newton methods for solving this problem, i.e. we linearize the functional around a current approximation and replace the Hessian by a suitable operator in order to obtain well‐posed subproblems in each step of the iteration.

These anisotropic subproblems are solved using a multigrid solver. Due to the anisotropy in the coefficients of the underlying equations, standard multigrid solvers suffer from poor convergence rates. We discuss modifications to the multigrid components, specifically to the smoothing procedure, the interpolation and the coarse grid correction. Numerical results that demonstrate the improvements obtained with these new components are given. Copyright © 2006 John Wiley & Sons, Ltd.