Phase Root Seeking and the Cramer-Rao-Lower Bound for Strain Estimation

With the Phase-Root-Seeking algorithm a new and very fast algorithm for time delay estimation was recently introduced, permitting the estimation of strain images in real-time. In this paper the accuracy of the real-time strain imaging concept is investigated by the most rigorous approach, i.e. a comparison to the theoretical accuracy limit: the Cramer-RaoLower-Bound. Simulations show, that this limit can be approximately reached by carefully selecting window length and window shift for time delay estimations and using a generalized least square estimator for the estimation of strain from time delays. INTRODUCTION delay estimation, the Phase Root Seeking algorithm Recently we introduced a new concept for time used for time-delay estimation [2, 51 this algorithm [6, 71. In contrast to conventional approaches which looks for the root of the phase of the correlation function of the analytic (complex) signals, instead of finding the maximum of the correlation function of the rf-signals. The root can be determined very efficiently by a modified Newton Iteration, leading to a very fast and accurate algorithm. Using this algorithm the first real-time strain imaging system was developed by our group [8]. In this system strain estimation and imaging is performed by a conventional desktop PC parallel to B-mode imaging. In order to demonstrate the noise performance of the be compared to various former algorithms. However, estimator used for strain estimation, the variance can a comparison of the estimation error to its theoretical lower limit, the Cramer-Rao Lower Bound, is preferred in this paper, since it demonstrates the performance independently from parameters used in other algorithms, implementation details and possible future modifications. In [6] we showed, that Phase Root Seeking, as a 0-7803-5722-1/99/$10.00