# A New Method for Detecting Weld Stability Based on Color Digital Holography
## 3 Experiments and Results
### Evaluation of Speckle Noise Reduction Algorithms  
To minimize speckle noise, the research used traditional spatial and frequency domain algorithms alongside deep learning algorithms to denoise the wrapped phase difference, including the Median, Block Matching and 3D filtering (BM3D), 2-D Windowed Fourier transform (WFT2F), CycleGAN and 4f-CycleGAN algorithms. These algorithms were used to denoise the wrapped phase of the red channel in Figure 5a, and the results are shown in Figure 6.  
As shown in Figure 6, the boundaries of the wrapped phase obtained by the median and BM3D algorithm are still fuzzy and discontinuous. The WFT2F algorithm outperforms the BM3D algorithm. In the results obtained with the WFT2F algorithm, the boundaries of the wrapped phase are clear and continuous. However, residual speckle noise persists, and there are line-like streaks due to incomplete noise reduction in areas of the phase distribution that are relatively flat. In the results obtained from the CycleGAN and 4f-CycleGAN algorithms, the wrapped phase appears smooth, with clear and continuous boundaries. Overall, deep learning algorithms are superior to traditional spatial and frequency domain algorithms, which is also the reason why deep learning algorithms have been widely used in recent years. Figure 4: Holograms of (**a**) lap-jointed plate, (**b**) butt-jointed plate, (**c**) defective butt-jointed plate. (1600 pixels \(\times\) 1200 pixels, 5.52 mm \(\times\) 4.14 mm). Figure 5: Wrapped phases after noise masking of (**a**) lap-jointed plate (293.67 N-297.59 N, 1024 pixels \(\times\) 256 pixels, 3.7 cm \(\times\) 0.9 cm), (**b**) butt-jointed plate (293.67 N-297.59 N, 1024 pixels \(\times\) 256 pixels, 3.1 cm \(\times\) 0.8 cm), (**c**) defective butt-jointed plate (293.87 N-294.26 N, 1024 pixels \(\times\) 256 pixels, 3.6 cm \(\times\) 0.9 cm). The sum of the peak signal-to-noise ratio (PSNR) was used to quantify the denoising results of these algorithms [31]. Table 1 shows the PSNR of five denoising algorithms for lap-jointed aluminum alloy plates. The sum of PSNR of the 4f-CycleGAN algorithm based on deep learning has a maximum value of 140.6 dB, indicating that its denoising result is the best. The sum of PSNR of the CycleGAN algorithm based on deep learning is 140.19 dB, indicating its better denoising result. The sum of PSNR of the WFT2F algorithm based on the frequency domain is 113.79 dB. The sum of PSNR of BM3D and median denoising algorithms based on the airspace is 26.88 dB and 70.82 dB, respectively, indicating that their denoising results are poor. Therefore, deep learning algorithms have better denoising results than traditional spatial and frequency domain algorithms for the detection system. The following research only uses the BM3D algorithm, the WFT2F algorithm, and the 4f-CycleGAN algorithm to study the denoising results. Table 2 shows the PSNR of these algorithms for the butt-jointed aluminum alloy plate. The sum of PSNR for the 4f-CycleGAN algorithm in deep learning is the maximum, which is 118.81 dB, indicating that the 4f-CycleGAN algorithm has the best denoising result on the wrapped phase of the butt-jointed aluminum alloy plate. \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Median** & **BM3D** & **WFT2F** & **CycleGAN** & **4f-CycleGAN** \\ \hline PSNR\_R & 25.83 & 8.49 & 44.58 & 47.35 & 47.54 \\ PSNR\_G & 22.51 & 9.36 & 34.19 & 48.42 & 51.41 \\ PSNR\_B & 22.48 & 9.03 & 35.02 & 44.42 & 41.65 \\ SUM & 70.82 & 26.88 & 113.79 & 140.19 & 140.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PSNR (dB) of several algorithms for the lap-jointed aluminum alloy plate. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **BM3D** & **WFT2F** & **4f-CycleGAN** \\ \hline PSNR\_R & 8.90 & 37.50 & 36.53 \\ PSNR\_G & 10.09 & 35.82 & 44.04 \\ PSNR\_B & 10.23 & 30.00 & 38.24 \\ SUM & 29.22 & 103.32 & 118.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PSNR (dB) of several algorithms for the butt-jointed aluminum alloy plate.