Two dimensional analytic wavelet thresholding and its application to ultrasonic pulse-echo B-scan denoising

Ultrasonic signals acquired from field experiments are often noisy. In pulse-echo setup, the wedge echo is also present which corrupts the received signal further. In this paper, we use the two-dimensional stationary wavelet transform and analytic thresholding for removing the random noise and the wedge noise. In order to apply the analytic thresholding, we need to calculate 2D analytic signal. Since there is no regular generalization of the analytic signal to two dimensions, we address this problem for the case of the ultrasonic pulse echo setup. We utilize a simulated signal and an experimental signal to evaluate the performance of the proposed denoising method. The experimental results show that the proposed method is able to reveal the signature of a crack as small as 0.1 mm.