Matching pursuit for decomposition and approximation of ultrasonic pulse-echo wavelet and its application in ultrasonic nondestructive evaluation.

The estimation of the time of arrival (TOA) and/or time of flight of the ultrasonic echoes is essential in ultrasonic nondestructive evaluation. In this paper, matching pursuit method has been used to analyze noisy ultrasonic pulse-echo wavelet and decompose the noisy pulse-echo wavelet into unit-norm vectors. The error ratio of the mean square is used to monitor the acceptability of the unit-norm vector obtained by the matching pursuit performance. A matched filter can be designed by using the time reversal of the approximation pulse-echo wavelet obtained by the reconstruction result with several large coefficient decomposed unit-norm vectors. After performing the matched filter, the part of the signal related to the electrical noise will be removed leaving only the correlated portion of the ultrasonic echoes. Then no initial phase have been contained in the processed ultrasonic echoes. Therefore, the TOA can be estimated directly from the peaks of the representation of the processed signal. Numerical simulations and experimental results make evidence the good performance of the proposed approach which has good effect of noise suppression and results in much improved accuracy in the estimation of echo arrival time.