Model based estimation of ultrasonic echoes: Analysis, algorithms, and applications.

摘要

The patterns of ultrasonic echoes represent valuable information pertaining to the geometric shape, size and orientation of the reflectors as well as the microstructure of the propagation path. Accurate estimation of the ultrasonic echo pattern is essential in determining the object and/or propagation path properties. In this research, we model ultrasonic echoes in terms of superimposed Gaussian echoes corrupted by noise. Each Gaussian echo in the model is a nonlinear function of a set of parameters: echo bandwidth, arrival time, center frequency, amplitude and phase. These parameters are sensitive to the echo shape and can be linked to the physical properties of reflectors and frequency characteristics of the propagation path. We address the estimation of model parameters in the Maximum Likelihood Estimation (MLE) framework, utilizing Expectation Maximization (EM) based algorithms. The EM algorithms translate the complicated superimposed echoes estimation into isolated echo estimations, hence providing computational versatility. The algorithm outperforms the LS methods in terms of independence to the initial guess, convergence to the optimal solution, and is able to resolve closely spaced overlapping echoes. In performance analysis of this estimation method, we derived analytical Cramer-Rao Lower Bounds (CRLB) on the model parameters, and compared the variances of estimators against these bounds, utilizing Monte-Carlo simulations. We observed that the parameter estimators are unbiased and their variances attain the CRLB for SNR as low as 2.5 dB.; Model based estimation provides high resolution and accurate estimates for ultrasonic echo parameters (i.e., time-of-flight, amplitude, center frequency, bandwidth, and phase). Furthermore, it offers a solution to the deconvolution problem for restoration of the target response (i.e., ultrasonic reflection and transmission properties of materials) from the backscattered echoes. It makes deconvolution possible in the presence of significant noise and can restore closely spaced overlapping echoes beyond the resolution of the measuring system. These claims are demonstrated in various ultrasonic applications such as transducer pulse-echo wavelet estimation, sub-sample time delay estimation, and thickness sizing of thin layers.