Adaptive Regularization of Ill-Posed Problems: Application to Non-rigid Image Registration
Abstract
We introduce an adaptive regularization approach. In contrast to conventional Tikhonov regularization, which specifies a fixed regularization operator, we estimate it simultaneously with parameters. From a Bayesian perspective we estimate the prior distribution on parameters assuming that it is close to some given model distribution. We constrain the prior distribution to be a Gauss-Markov random field (GMRF), which allows us to solve for the prior distribution analytically and provides a fast optimization algorithm. We apply our approach to non-rigid image registration to estimate the spatial transformation between two images. Our evaluation shows that the adaptive regularization approach significantly outperforms standard variational methods.
Cite
@article{arxiv.0906.3323,
title = {Adaptive Regularization of Ill-Posed Problems: Application to Non-rigid Image Registration},
author = {Andriy Myronenko and Xubo Song},
journal= {arXiv preprint arXiv:0906.3323},
year = {2009}
}