A FUNDAMENTAL LIMIT ON THE PERFORMANCE OF CORRELATION-BASED PHASE CORRECTION AND FLOW ESTIMATION TECHNIQUES

Cross correlation and similar operations are used in ultrasonic imagin g to estimate blood or soft tissue motion in one or more dimensions an d to measure echo arrival time differences for phase aberration correc tion. These estimates are subject to large errors known as false peaks and smaller magnitude errors known as jitter. While false peaks can s ometimes 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 ex pressions which predict the magnitude of jitter for 1-D and 2-D proble ms using both radio frequency (RF) and envelope detected data. One-dim ensional simulation results are presented which closely match theoreti cal predictions. These results indicate that for typical clinical cond itions axial jitter for detected data is approximately five times grea ter than that for RF data. Lateral jitter is approximately ten times g reater than axial jitter for RF data. Examples are presented which uti lize these results to predict the performance of phase aberration corr ection and flow estimation systems.