Overview

The fundamental idea of this method is to combine a local optimisation method (Powell's [Press et al., 1995]) with an initial search. Furthermore, the search is tuned so that it is computationally feasible. In particular, our implementation of the whole optimisation method executes in approximately 40 minutes on a modern PC.

There are four different sub-sampling levels that are used by the optimisation algorithm: $n_0 = 8, \, n_1 = 4, \, n_2 = 2, \, n_3 = 1$. Initially, 8mm cubed voxels are used and a full search is conducted over the rotation angles. Following this, various local optimisation are performed with a variety of starting points in the local neighbourhood of the best points identified in the search. These local optimisations are done using 4mm, 2mm and finally 1mm cubed voxels. Each of these stages is described below in more detail.