# A Convolutional Neural Network SAR Image Denoising Algorithm Based on Self-Learning Strategies
## 3 Experiment
### Experimental Results  
Based on the above research plan, two quantitative evaluation indicators for denoising effect are calculated: Signal-to-Noise Ratio (SNR), Background Suppression Factor (BSF) and Structural Similarity Index (SSIM). SNR measures the ratio of the signal power to the noise power in the denoised image. It is a widely used metric to evaluate the quality of the denoised image. For clean image \(x_{c}\), noise image \(x_{n}\) and the denoised image y, (i, j) is the coordinates of a pixel. \[SNR=10 log_{10}\left(\frac{\sum_{i,j}x_{c}\left(i,j\right)^{2}}{\sum_{i,j}\left[ x_{c}\left(i,j\right)-y(i,j)\right]^{2}}\right) \tag{5}\]  
BSF measures the improvement in noise suppression achieved by the denoising algorithm. It is defined as the ratio of the noise level in the original noisy image to the noise level in the denoised image. The BSF is calculated as  
\[BSF=10 log_{10}\left(\frac{\sigma_{noise}^{2}}{\sigma_{denoise}^{2}}\right) \tag{6}\]  
\[\sigma_{noise}^{2}=\sqrt{\frac{1}{HW}\sum_{i=1}^{H}\sum_{j=1}^{W}\left(x_{ residual}\left(i,j\right)-\mu_{residual}\right)^{2}} \tag{7}\]  
Figure 5: Visualization of denoising methods. where \(\sigma_{noise}^{2}\) is the variance between the noised image \(x_{n}\) and the clean image \(x_{c}\), \(x_{residual}=x_{n}-x_{c}\), \(\mu_{residual}\) is the mean of the residual noise. \(\sigma_{noise}^{2}\) is the variance between the denoised image y and the clean image \(x_{c}\). SSIM measures the structural similarity between the clean image \(x_{c}\) and the denoised image y. It considers luminance, contrast, and structure. \[SSIM=\frac{\left(2\mu_{x_{c}}\mu_{y}+C_{1}\right)\left(2\sigma_{x_{c}y}+C_{2} \right)}{\left(\mu_{x_{c}}^{2}+\mu_{y}^{2}+C_{1}\right)\left(\sigma_{x_{c}}^{2 }+\sigma_{y}^{2}+C_{2}\right)} \tag{8}\]  
where \(\mu_{x_{c}}\) is the mean of the clean image, \(\mu_{y}\) is the mean of the denoised image, \(\sigma_{x_{c}}^{2}\) is the variance of the clean image, \(\sigma_{y}^{2}\) is the variance of the denoised image, \(\sigma_{x,y}\) is the covariance between \(x_{c}\) and y, \(C_{1}\) and \(C_{2}\) are constants for stability. The experimental results are shown in Table 1, indicating that it is difficult to achieve good results on SAR images using only solid color block images for training. It is only effective for Poisson noise and salt and pepper noise and is basically ineffective for stripe noise. Therefore, in the next stage, the original SAR image and the noise superimposed image will be used as sample pairs to train the model and further improve the improvement effect of the model on SAR images. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Noise Category** & **Noise** & **Denoise** & **BSF** \\ \hline Original image & & & 1.87 \\ Gaussian noise & & & 1.43 \\ Poisson noise & & & 3.33 \\ Salt and pepper noise & & & 1.26 \\ Coherent noise & & & 1.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examples of different denoise performance and BSF. To assess the performance of denoising algorithms under realistic noise conditions, five classic image denoising methods were rigorously evaluated on the simulation dataset, a benchmark designed to replicate complex noise patterns encountered in practical imaging scenarios. Additionally, a quantitative evaluation was conducted on a DnCNN-based denoising model (a deep convolutional neural network architecture widely used for noise suppression), with results summarized in Table 2. When directly deploying the DnCNN model with pre-trained parameters (trained on generic grayscale images under blind noise assumptions), its denoising efficacy on the dataset was suboptimal. The model achieved a signal-to-noise ratio (SNR) of 18.25 dB, a BSF of 2.86 and an SSIM of 0.65, both metrics indicating limited noise reduction capability.