A Stochastic Quasi-Newton Method for Non-Rigid Image Registration

Image registration is often very slow because of the high dimensionality of the images and complexity of the algorithms. Adaptive stochastic gradient descent (ASGD) outperforms deterministic gradient descent and even quasi-Newton in terms of speed. This method, however, only exploits first-order information of the cost function. In this paper, we explore a stochastic quasi-Newton method (s-LBFGS) for non-rigid image registration. It uses the classical limited memory BFGS method in combination with noisy estimates of the gradient. Curvature information of the cost function is estimated once every L iterations and then used for the next L iterations in combination with a stochastic gradient. The method is validated on follow-up data of 3D chest CT scans (19 patients), using a B-spline transformation model and a mutual information metric. The experiments show that the proposed method is robust, efficient and fast. s-LBFGS obtains a similar accuracy as ASGD and deterministic LBFGS. Compared to ASGD the proposed method uses about 5 times fewer iterations to reach the same metric value, resulting in an overall reduction in run time of a factor of two. Compared to deterministic LBFGS, s-LBFGS is almost 500 times faster.