A robust time delay estimation method for ultrasonic echo signals and elastography

Modern medicine cannot ignore the significance of elastography in diagnosis and treatment plans. Despite improvements in accuracy and spatial resolution of elastograms, robustness against noise remains a neglected attribute. A method that can perform in a satisfactory manner under noisy conditions may prove useful for various elastography methods. Here, we propose a method based on eigenvalue decomposition (EVD). In this method, the estimated time delay is defined as the index of the maximum element in the eigenvector that corresponds to the minimum eigenvalue in the covariance matrix of the received signal. Moreover, the implementation of the least-squares (LS) solution and the lower-upper (LU) decomposition contributes to improving the speed of computation and the accuracy of the estimation under low signal-to-noise ratio (SNR) conditions. To assess the performance of the proposed algorithm, it is evaluated along with generalized cross-correlation (GCC) and EVD. The simulation results clearly confirm that the jitter variance achieved in the proposed algorithm outperforms GCC and EVD in the proximity of the Cramer-Rau lower band. Moreover, our algorithm provides satisfactory performance in terms of variance and bias against sub-sample delay at low SNRS. According to the experimental results, the calculated values of the elastographic signal-to-noise ratio (SNRe) and the elastographic contrast-to-noise ratio (CNRe) of the proposed algorithm were 16.7 and 20.09, respectively, clearly better than the values of the other two methods. Furthermore, the proposed algorithm offers less execution time (about 30% of GCC), with a computational complexity equal to GCC and better than EVD.