A Sparse Matrix Formalism for Non-Rigid Motion Correction
Batchelor P, Atkinson D, G. Hill D, Larkman D, Hajnal J, Irrarazaval P, Hansen M
University College London
Here we discuss a method to perform general non-rigid motion correction of multi-shot images, even when the inverse motion is not known (but the motion itself is found with the help of e.g. a navigator). We explicitly construct a sparse system for the unknown image, whose right hand-side is the motion-ghosted image. We make the assumption that motions happen between shots, in a multishot context, where each shot is a set of regularly spaced lines. The influence of sparseness on computation time and accuracy is studied, and we show an example of correction of a simulated ghosted image, where the motion at each shot is a spline deformation.