"An efficient preconditioner for stochastic gradient descent optimization of image registration"

Yuchuan Qiao, Boudewijn P.F Lelieveldt and Marius Staring

Abstract

Stochastic gradient descent (SGD) is commonly used to solve (parametric) image registration problems. In case of badly scaled problems, SGD however only exhibits sublinear convergence properties. In this paper we propose an efficient preconditioner estimation method to improve the convergence rate of SGD. Based on the observed distribution of voxel displacements in the registration, we estimate the diagonal entries of a preconditioning matrix, thus rescaling the optimization cost function. The preconditioner is efficient to compute and employ, and can be used for mono-modal as well as multi-modal cost functions, in combination with different transformation models like the rigid, affine and B-spline model. Experiments on different clinical data sets show that the proposed method indeed improves the convergence rate compared to SGD with speedups around 2-5 in all tested settings, while retaining the same level of registration accuracy.

Source code

The source code of the methods described in this paper can be found in the image registration toolkit elastix, available at https://github.com/SuperElastix/elastix.

BibTeX entry