Ultrasonic parameter estimation using the Maximum Likelihood Estimation

The estimation of the backscattered echo was performed using the Maximum Likelihood Estimation (MLE). The backscattered ultrasonic echo is modeled as a nonlinear function of a set of parameters using the Gaussian echo model corrupted with an additive noise. Because of the white Gaussian noise (WGN) assumption, the estimation problem reduces to a least squares estimation. Thus, the nonlinear least square curve fitting with the Levenberg-Marquardt (LM) optimization algorithm was tested in the estimation procedure. The results are compared with existing results from the literature. To improve the goodness of the fit, the multivariate denoising procedure were applied as a preprocessing operation. Then, the efficiency and robustness of the LM algorithm are evaluated for both denoised and noisy signals.