Iterative autocorrelation motion estimation with application to elasticity imaging

Precise, robust and efficient motion estimation is the key to high quality strain imaging. Two are the main estimation techniques: (1) spatial-shift estimation using block matching, and (2) phase-shift estimation. The phase-shift estimators are more robust but are limited by phase aliasing. The scan depths of elastography imaging can be up to 300 wavelengths, and even moderate average strains of 0.5-1% result in displacements of several wavelengths. Several efficient methods have been created over the years to overcome the aliasing limit, but they often employ searching and tracking which are difficult to be implemented efficiently on graphical processing units. This paper presents an iterative algorithm for phase estimation using autocorrelation. In the first stage the autocorrelation is estimated for lag 0 for all pixels in the image. Then a phase-unwrapping algorithm is applied, and the unwrapped phase is converted to displacement. The center frequency used in the conversion is calculated using a 2-nd order polynomial which describes the depth-dependent shift in center frequency. This polynomial needs to be estimated once for every setup using an uniform speckle phantom. The displacement is quantized by the spatial sampling interval. The autocorrelation function is estimated at the quantized spatial lags. The precision of the autocorrelation estimate varies depending on the magnitude of the phase which leaves visible horizontal stripes at the transition from one lag to another. Finally we apply a deglitching algorithm to compensate for the change in precision at the boundaries between two lags.