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To remove the noise in the echo signals of ultrasonic pulse-echo testing, this paper puts forward a denoising algorithm based on the generalized S transform (GST) and singular value decomposition (SVD). Firstly, the ultrasonic echo signals were subjected to the GST, yielding the time-frequency matrix of the signals. Next, the matrix was taken as the Hankel matrix, and went through the SVD. The threshold for singular values to be zeroed was determined by the ratio between singular entropy increments. After zeroing the singular values representing the noise, the resulting denoised 2D time-frequency matrix was subjected to the inverse GST, generating the denoised echo signals. Our method was applied to denoise the simulated ultrasonic echo signals with different signal-to-noise ratios (SNRs), and compared with the wavelet soft thresholding (WST) method. The comparison show that our method outperformed the WST, especially in denoising the signals with low SNR. In addition, a scanning acoustic microscopy (SAM) system was designed for the experimental verification of our method. The C-scan image with our method was much better than that without our method. Hence, our method was proved feasible and effective.

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Weighted compact nonlinear schemes (WCNS) [Deng and Zhang, JCP 165(2000): were developed to improve the performance of the compact high-order nonlinear schemes (CNS) by utilizing the weighting technique originally designed for WENO schemes, and excellent shock capturing capability and high resolution are achieved. Various work has been given for further improving the performance of WC-NSs since then. In this work, the ENO-like stencil selection procedure of Targeted ENO schemes [Fu et al. JCP 305(2016):333-359] is introduced for interpolating midpoint variables, targeting compact nonlinear schemes which fully abandon the oscillatory stencils crossing discontinuities, and directly apply optimal linear weights when the flow field is smooth, such that the optimal numerical resolution is fully recovered in smooth flow field. Several canonical numerical cases of scalar equations and the Euler equations of gas dynamics are given to examine the performance of the presented method.