A fundamental limit on delay estimation using partially correlated speckle signals

Delay estimation is used in ultrasonic imaging to estimate blood or soft tissue motion, to measure echo arrival time differences for phase aberration correction, and to estimate displacement for tissue elasticity measurements. In each of these applications delay estimation is performed using speckle signals which are at least partially decorrelated relative to one another. Delay estimates which utilize such data 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. The authors apply the Cramer-Rao Lower Bound to derive an analytical expression which predicts the magnitude of jitter errors incurred when estimating delays using radio frequency (RF) data from speckle targets. The analytical expression presented includes the effects of signal decorrelation due to physical processes, corruption by electronic noise, and a number of other factors. Simulation results are presented which show that the performance of the normalized cross correlation algorithm closely matches theoretical predictions. These results indicate that for poor signal to noise ratios (0 dB) a small improvement in signal to noise ratio can dramatically reduce jitter magnitude. At high signal to noise ratios (30 dB) small amounts of signal decorrelation can significantly increase the magnitude of jitter errors.<>