Phase-sensitive 2D motion estimators using frequency spectra of ultrasonic echoes

Recently, high-frame-rate ultrasound has been extensively studied for measurement of tissue dynamics, such as pulsations of the carotid artery and heart. Motion estimators are very important for such measurements of tissue dynamics. In high-frame-rate ultrasound, the tissue displacement between frames becomes very small owing to the high temporal resolution. Under such conditions, the speckle tracking method requires high levels of interpolation to estimate such a small displacement. A phase-sensitive motion estimator is feasible because it does not suffer from the aliasing effect by such a small displacement and does not require interpolation to estimate a sub-sample displacement. In the present study, two phase-sensitive 2D motion estimators, namely, paired 1D motion estimators and 2D motion estimator with shifted cross spectra, were developed. Phase-sensitive motion estimators using frequency spectra of ultrasonic echoes have already been proposed in previous studies. However, such methods had not taken into account the ambiguity of the frequency of each component of the spectrum. We have proposed a method, which estimates the mean frequency of each component of the spectrum, and the proposed method was validated by a phantom experiment. The experimental results showed that the bias errors in the estimated motion velocities of the phantom were less than or equal to (11.5% in lateral, 2.0% in axial) by the proposed 1D paired motion estimators and (3.0%, 2.0%) by the proposed 2D motion estimators, both of which were significantly smaller than (14.0%, 3.0%) of the conventional phase-sensitive 2D motion estimator.