Wavelet Cycle Spinning Denoising of NDE Ultrasonic Signals Using a Random Selection of Shifts

Wavelets are a powerful tool for signal and image denoising. Most of the denoising applications in different fields were based on the thresholding of the discrete wavelet transform (DWT) coefficients. Nevertheless, DWT transform is not a time or shift invariant transform and results depend on the selected shift. Improvements on the denoising performance can be obtained using the stationary wavelet transform (SWT) (also called shift-invariant or undecimated wavelet transform). Denoising using SWT has previously shown a robust and usually better performance than denoising using DWT but with a higher computational cost. In this paper, wavelet shrinkage schemes are applied for reducing noise in synthetic and experimental non-destructive evaluation ultrasonic A-scans, using DWT and a cycle-spinning implementation of SWT. A new denoising procedure, which we call random partial cycle spinning (RPCS), is presented. It is based on a cycle-spinning over a limited number of shifts that are selected in a random way. Wavelet denoising based on DWT, SWT and RPCS have been applied to the same sets of ultrasonic A-scans and their performances in terms of SNR are compared. In all cases three well known threshold selection rules (Universal, Minimax and Sure), with decomposition level dependent selection, have been used. It is shown that the new procedure provides a good robust denoising performance, without the DWT fluctuating performance, and close to SWT but with a much lower computational cost.