A FUNDAMENTAL LIMIT ON DELAY ESTIMATION USING PARTIALLY CORRELATED SPECKLE SIGNALS

Delay estimation is used in ultrasonic imaging to estimate blood or so ft tissue motion, to measure echo arrival time differences for phase a berration correction, and to estimate displacement for tissue elastici ty measurements. In each of these applications delay estimation is per formed 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 err ors known as jitter. While false peaks can sometimes be removed throug h nonlinear processing, jitter errors place a fundamental limit on the performance of delay estimation techniques. This paper applies the Cr amer-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 express ion presented includes the effects of signal decorrelation due to phys ical processes, corruption by electronic noise, and a number of other factors. Simulation results are presented which show that the performa nce of the normalized cross correlation algorithm closely matches theo retical predictions. These results indicate that for poor signal to no ise ratios (O dB) a small improvement in signal to noise ratio can dra matically reduce jitter magnitude. At high signal to noise ratios (30 dB) small amounts of signal decorrelation can significantly increase t he magnitude of jitter errors.