Parameter estimation of multiple interfering echoes using the SAGE algorithm

Parametric modeling of a measured signal in terms of frequency dispersion, velocity, amplitude fading and echo skewness can be used as a quantitative technique for nondestructive evaluation. A simple model with a fixed number of parameters often performs inadequately when the ultrasonic wavelet is propagated through inhomogeneous materials and/or reflected by complex objects. In this study, we model the detected ultrasonic signal as a superposition of many Gaussian echoes corrupted with measurement noise. To estimate the parameters of multiple Gaussian echoes, a Space Alternating Generalized Expectation Maximization (SAGE) algorithm has been developed. In performance evaluation of the SAGE algorithm, Monte-Carlo simulation has been used. The estimated parameters have been found to be unbiased and their variances achieve analytical Cramer-Rao Lower Bounds (CRLB) for Signal-to-Noise Ratio (SNR) as low as 3 dB. The CRLB also constitutes the resolution bounds on the estimated parameters. Furthermore, the SAGE algorithm has been applied to experimental ultrasonic data consisting of multiple interfering echoes. It has been observed that the model fits accurately to the measured signal (estimation SNR is as high as 24 dB) and the estimated parameters display a high resolution and accurate characterization of the measurement.