Phase-sensitive 2-D speckle tracking

After ultrasonic RF signal synthesis, a phase-sensitive correlation-based 2-D speckle tracking algorithm was applied to the RF data to estimate the displacement between the frames [20]. Frame-to-frame axial and lateral displacements were estimated from the position of the maximum correlation coefficient from the cross-correlation on the baseband complex signals derived from the RF data.

The ultrasound speckle size was estimated to be 0.270 mm in the axial direction and 0.586 mm in the lateral direction from the 2-D correlation function of the baseband signals. The search kernel of the speckle tracking was set to be about the ultrasound speckle size for optimal displacement estimation with minimum variance [20]. Axial displacements were then refined using the phase zero-crossing of the complex correlation functions. To enhance the signal-to-noise ratio with reasonable spatial resolution, the adjacent correlation functions were filtered using 0.781 mm (lateral) by 0.308 mm (axial) separable Hanning filter. The search region was 0.781 mm in both dimensions. The frame-to-frame axial displacements were then accumulated over the entire 105 frames reference to the original geometry, to estimate the total displacement [21]. With the accumulation of frames, the displacement SNR was enhanced by reducing any uncorrelated errors in the axial displacement estimates [20].