Preconditioned stochastic gradient descent optimisation for monomodal image registration

Abstract

We present a stochastic optimisation method for intensity-based monomodal image registration. The method is based on a Robbins-Monro stochastic gradient descent method with adaptive step size estimation, and adds a preconditioning matrix. The derivation of the preconditioner is based on the observation that, after registration, the deformed moving image should approximately equal the fixed image. This prior knowledge allows us to approximate the Hessian at the minimum of the registration cost function, without knowing the coordinate transformation that corresponds to this minimum. The method is validated on 3D fMRI time-series and 3D CT chest follow-up scans. The experimental results show that the preconditioning strategy improves the rate of convergence. © 2011 Springer-Verlag.