## 5 Conclusions  
This paper focuses on the denoising method in digital shearography. A sine-cosine transform wavelet threshold denoising method based on the sym4 basis function and threshold related to noise intensity is proposed. According to the comparative analysis of the speckle suppression index, the decomposition level with the best denoising effect is determined in the proposed method. The experimental results show that the denoising effect of the proposed method is better than that of the sine-cosine transform average denoising method with the similar execution time. Furthermore, the proposed method can adaptively set the threshold to process the speckle-interferometric patterns without artificially setting the mask and iterations compared to the sine-cosine transform average denoising method. This method can realize fast denoising and reserve phase reversal information well. It is beneficial to unwrap the phase information accurately. Simulation  
\begin{table}
\begin{tabular}{c c} \hline \hline
**The Pattern** & **The Denoising Threshold** \\ \hline (a)—DS-sine pattern & 3.544 \\ (a)—DS-cosine pattern & 3.885 \\ (d)—DS-sine pattern & 3.730 \\ (d)—DS-cosine pattern & 4.051 \\ (g)—DS-sine pattern & 2.952 \\ (g)—DS-cosine pattern & 3.120 \\ (j)—DS-sine pattern & 3.161 \\ (j)—DS-cosine pattern & 3.109 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The denoising threshold of each sine and cosine patterns.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**The Pattern** & **Execution Time/s** & **SSI** & **PSNR** & **SSIM** \\ \hline (a)—DS-SCT-wavelet & \(\sim\)1.850 & 0.064 & 41.370 & 0.884 \\ \hline (a)—DS-SCT-average & \(\sim\)1.850 & 0.074 & 40.380 & 0.886 \\ \hline (d)—DS-SCT-wavelet & \(\sim\)1.900 & 0.009 & 40.571 & 0.852 \\ \hline (d)—DS-SCT-average & \(\sim\)1.900 & 0.024 & 40.618 & 0.853 \\ \hline (g)—DSPI-SCT-wavelet & \(\sim\)1.950 & 0.155 & 42.031 & 0.944 \\ \hline (j)—DSPI-SCT-wavelet & \(\sim\)1.950 & 0.205 & 42.068 & 0.945 \\ \hline (j)—DSPI-SCT-wavelet & \(\sim\)2.100 & 0.210 & 41.339 & 0.948 \\ \hline (j)—DSPI-SCT-average & \(\sim\)2.100 & 0.233 & 42.437 & 0.953 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of SSI after the sine–cosine transform wavelet threshold denoising method and sine–cosine transform average denoising method when execution time is similar.  
analysis and experimental results verify the effectiveness of the proposed method. This method can play an important role in practical application scenarios such as defect detection, stress/strain monitoring, life prediction of the specimen, etc. In the next steps of the research, we will perfect the shearography-interferometric phase fringe patterns simulation algorithm to provide support for the optimization of the denoising algorithm, deeply explore the influence of different wavelet basis functions on the denoising effect, and use parallel computing to further improve the denoising efficiency of the algorithm.  
Conceptualization, Y.G., J.L. and L.C.; methodology, Y.G. and X.Z.; software, R.B.; validation, Y.G., Z.X. and S.T.; formal analysis, Y.G.; investigation, X.Z.; resources, L.C.; data curation, J.L.; writing--original draft preparation, Y.G.; writing--review and editing, L.C.; visualization, R.B.; supervision, J.L. and L.C.; project administration, L.C.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (No. 51535003 and No. 62205316) and Local Science and Technology Development Fund Projects Guided by the Central Government, China (No. 2022 YDP065).  
Not applicable.  
This work was supported by Standardization and Testing Center, Laser Fusion Research Center, China Academy of Engineering Physics.  
The authors declare no conflict of interest.