Phase-based block matching applied to motion estimation with unconventional beamforming strategies

A phase-based block matching method adapted to motion estimation with unconventional beamforming strategies is presented. The unconventional beamforming technique used allows us to obtain 2-D RF images with axial and lateral modulations. Based on these images, we propose a method that uses phase images instead of amplitude images. This way of proceeding allows us to provide an analytical solution to the local displacement estimation so that no minimization of a classical cost function is used for the local estimation. For this reason, the local estimator is directly applied to signals, without the need to process a complex cross-correlation function, as is done with most of the phase shift estimators. In this paper, the method is applied to elastography. Results with simulated data show that a downsampling of axial and lateral modulated signals leads to very little change in the accuracy and in the spatial resolution of the proposed method. For example, for decimation factors of 2 in the axial direction and of 4 in the lateral direction, the mean axial absolute error is 3 mum. The same estimation with original images provides a mean axial error of 0.7 mum. The accuracy of the lateral motion is unchanged in this case. The accuracy of our method with downsampled signals is an important issue in the purpose of a real-time implementation. With experimental data, for the same level of estimation error, classical block matching using the maximum of cross correlation as a local estimator requires images that are 36 times larger (in number of pixels) and consequently a computational time roughly 10 times longer. Our phase block matching is also shown to provide 10 percent less error than a motion estimation method based on seeking the zero of the complex correlation function phase. Finally, it is shown that given the separability of the local estimator that we propose, our method can be applied on both n-D signals and classical RF ultrasound images. The phase block matching method presented was implemented in real time on an ultrasound research scanner.