A subspace identification extension to the phase correlation method [MRI application]

The phase correlation method (PCM) is known to provide straightforward estimation of rigid translational motion between two images. It is often claimed that the original method is best suited to identify integer pixel displacements, which has prompted the development of numerous subpixel displacement identification methods. However, the fact that the phase correlation matrix is rank one for a noise-free rigid translation model is often overlooked. This property leads to the low complexity subspace identification technique presented here. The combination of noninteger pixel displacement identification without interpolation, robustness to noise, and limited computational complexity make this approach a very attractive extension of the PCM. In addition, this approach is shown to be complementary with other subpixel phase correlation based techniques.