Fundamental limit on the performance of correlation based phase correction and flow estimation techniques
Cross correlation and similar operations are used in ultrasonic imaging to estimate blood or soft tissue motion in one or more dimensions and to measure echo arrival time differences for phase aberration correction. These estimates are subject to large errors known as false peaks and smaller magnitude errors known as jitter. While false peaks can sometimes be removed through nonlinear processing, jitter errors place a fundamental limit on the performance of delay estimation techniques. This paper applies the Cramer-Rao Lower Bound to derive analytical expressions which predict the magnitude of jitter for 1-D and 2-D problems using both radio frequency (RF) and envelope detected data. One-dimensional simulation results are presented which closely match theoretical predictions. These results indicate that for typical clinical conditions axial jitter for detected data is approximately five times greater than that for RF data. Lateral jitter is approximately ten times greater than axial jitter for RF data. Examples are presented which utilize these results to predict the performance of phase aberration correction and flow estimation systems.