Denoising of fast and weak transient signals using selected orthogonal wavelet transform

By modelling the laser ultrasonic signals consisting of fast transient echoes and noise, and by analysing the projection of the echoes and noise in the domain of the orthogonal wavelet transform (OWT) and the stationary wavelet transform (SWT), the paper presents a new denoising method, named the selected orthogonal wavelet transform, to produce better signal restoration. Instead of performing the normal single fixed OWT or the normal averaging operation of multiple OWTs in the SWT, the underlying principle of the proposed method is to reconstruct the signal by using the best set of the approximation coefficients retained at each transform scale according to its energy. By using a computer simulated laser ultrasonic signal as an example, the proposed denoising method is shown to produce a better signal with no false echoes and less amplitude attenuation.