Error bounds on ultrasonic scatterer size estimates

Precision errors that occur in estimating the average scatterer size from pulse-echo ultrasound waveforms are examined in detail. The method- independent lower bound on estimation error is found from the Cramer-Rao inequality for comparison with the predicted error for the measurement technique currently used to estimate scatterer sizes in soft biological tissues. The probability density function for the estimate is also derived. From these statistical analyses, strategies for designing experiments that minimize the error are discussed. It is shown that compared with biological variability, measurement errors in scatterer size estimates are relatively large. Consequently, there is reason to continue searching for more efficient estimators. Although the analysis and results are derived for Gaussian correlation models that have been used to study the function and structure of kidneys, generalization to include correlation models for other tissues is straightforward.