Cosine-Sine Modulated Filter Banks for Motion Estimation and Correction

We present a new motion estimation algorithm that uses cosine-sine modulated filter banks to form complex modulated filter banks. The motion estimation is based on phase differences between a template and the reference image. By using a non-downsampled version of the cosine-sine modulated filter bank, our algorithm is able to shift the template image over the reference image in the transform domain by only changing the phases of the template image based on a given motion field. We also show that we can correct small non-rigid motions by directly using the phase difference between the reference and the template images in the transform domain. We also include a first application in magnetic resonance imaging, where the Fourier space is corrupted by motion and we use the phase difference method to correct small motion. This indicates the magnitude invariance for small motions.