Shift Invariant Wavelet Denoising of Ultrasonic Traces

Abstract

Basic wavelet denoising techniques rely on a thresholding of the discrete wavelet transform (DWT) coefficients of the noisy signal. Some improvements in noise reduction efficiency can be obtained by the use of shift-invariant undecimated wavelet transforms (UWT). Ultrasonic grain noise is one of the most usual types of noise present in ultrasonic non-destructive evaluation. It comes from reflections in the material structure, and occupies a frequency band very similar to that of the echosignals of interest. In this work, new advances in the application of redundant wavelet transforms to ultrasonic grain noise reduction are presented. Wavelet denoising is applied to several sets of synthetic ultrasonic traces, which are obtained from a model that includes frequency dependent attenuation for both grain and flaw backscattered echoes, frequency dependent scattering from the grains, and an accurate model for the pulse-echo frequency response of the piezoelectric ultrasonic transducer. Two processors based on traditional DWT and alternative a trous UWT denosing have been implemented and compared, using level dependent thresholds (appropriate for correlated noise), soft thresholding, and Universal, SURE and Minimax threshold selection rules. The performances of the two processors are analyzed in terms of the mean value and standard deviation of the signal-to-noise ratio (SNR) of different sets of ultrasonic traces before and after denoising. It is shown that a trous UWT processing provides better results than DWT with a general tendency to higher quality of the resulting traces and greater robustness of the processing. It is also shown that the better performance of the UWT is mainly related to the redundancy of the representation, since there are not significant variations between the threshold values obtained with each processor.