# Denoising of Wrapped Phase in Digital Speckle Shearography Based on Convolutional Neural Network
## 3 Experiments
### The Denoising Effect on Simulated Images  
In order to test the training effect of the model more fully, this paper proposes a method to generate wrapped phases with different noise intensities. This work first performs low-pass filtering on the two speckle fields of Equations (1) and (2) by adjusting the aperture size in the 4f system [2], and the filtered speckle field intensity can be expressed as  
\[I_{1,2}=F^{-1}\{f(d)\times F[A\exp(i\varphi_{1,2})]\} \tag{20}\]  
where \(F\) represents the Fourier transform, \(F^{-1}\) represents the inverse Fourier transform, \(f(k_{1},k_{2})\) represents a low-pass filter. The speckle fringes (480 \(\times\) 480 pixels) with the different aperture sizes generate different speckle sizes, where the smaller selected aperture produces a larger speckle size. In addition, to evaluate the denoising performance of SDCNN on wrapped phases generated by apertures of different sizes, we conducted tests on 100 images and compared the results with the algorithms OBNLM, BM3D, and DNCNN. The test comparison results are illustrated in Figure 6; the test data is presented in Table 2.  
Figure 7 and Table 2 reveal that SDCNN significantly outperforms OBNLM, BM3D, and DNCNN in terms of denoising efficacy and the preservation of intricate details in speckle-corrupted maps. This phenomenon clearly demonstrates the strong generalization ability of SDCNN for effectively balancing noise reduction and detail preservation. Figure 6: SSIM and RMSE comparison between two loss functions on different input noise levels. An illustrative example, depicting the test results presented in Figure 8, reveals that SDCNN significantly outperforms OBNLM, BM3D, and DNCNN in terms of denoising efficacy and the preservation of intricate details in speckle-corrupted images. Figure 7: Denoising results on the wrapped phase of different aperture simulations: (**a**) noise image; (**b**) denoising result of OBNLM; (**c**) denoising result of BM3D; (**d**) denoising result of DNCNN; and (**e**) denoising result of SDCNN. Figure 8: Denoising results on images from the test dataset with different noise levels by different methods: (**a**) noise maps with different noise levels; (**b**) denoising results of OBNLM; (**c**) denoising results of BM3D; (**d**) denoising results of DNCNN; and (**e**) denoising results of SDCNN. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **Noise Level** & **PSNR (dB)** & **SSIM** & **RMSE** & **Time (s)** \\ \hline \multirow{3}{*}{OBNLM} & 25 & 20 & 0.76 & 0.1 & 85 \\  & 50 & 18.84 & 065 & 0.11 & 80.6 \\  & 75 & 17.63 & 0.56 & 0.13 & 79.63 \\  & 100 & 16.68 & 0.49 & 0.15 & 75.6 \\ \hline \multirow{3}{*}{BM3D} & 25 & 25 & 0.97 & 0.13 & 289 \\  & 50 & 23.07 & 0.95 & 0.30 & 290 \\  & 75 & 21.8 & 0.94 & 0.26 & 287 \\  & 100 & 21.46 & 0.93 & 0.18 & 292 \\ \hline \multirow{3}{*}{DNCNN} & 25 & 24.41 & 0.895 & 0.06 & 0.01 \\  & 50 & 23.50 & 0.864 & 0.07 & 0.01 \\  & 75 & 22.53 & 0.87 & 0.07 & 0.01 \\  & 100 & 21.84 & 0.866 & 0.08 & 0.01 \\ \hline \multirow{3}{*}{SDCNN} & 25 & 25.88 & 0.89 & 0.05 & 0.01 \\  & 50 & 24.78 & 0.92 & 0.06 & 0.01 \\ \cline{1-1}  & 75 & 23.64 & 0.88 & 0.06 & 0.01 \\ \cline{1-1}  & 100 & 22.16 & 0.89 & 0.07 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average PSNR(dB), SSIM, and results RMSE of different methods on simulated noise images with different noise level combinations \(\theta=1\) and \(\sigma=0,25,50,75,100\). The enlarged details, highlighted by the red border in the image, provide compelling evidence of this superiority. In Figure 8b, OBNLM performs well in denoising at lower noise levels, but its effectiveness diminishes significantly when the noise intensity is higher. In Figure 8c, BM3D demonstrates relative effectiveness in speckle-noise reduction while excelling at preserving fine details. However, the BM3D algorithm performs filtering in the transform domain, resulting in the appearance of pseudo-texture artifacts in the denoised images, which can affect the accuracy of phase unwrapping in the denoised images.