# Noise Suppressed Image Reconstruction for Quanta Image Sensors Based on Transformer Neural Networks
## 4 Experimental Results
### Network Analysis Experiments  
To explore the rationality of the network structure settings in this study, experiments were conducted to compare the configurations with and without Anscombe transform, with and without the IT component, in a combinatorial manner. The test datasets were Set12 [29] and BSD68 [29], with Noise level 1 (\(T=16\), \(K=4\), \(\sigma_{\text{read}}=0.2\)e-), Noise level 2 (\(T=16\), \(K=4\), \(\sigma_{\text{read}}=0.4\)e-), Noise level 3 (\(T=16\), \(K=2\), \(\sigma_{\text{read}}=0.2\)e-), Noise level 4 (\(T=16\), \(K=1\), \(\sigma_{\text{read}}=0.4\)e-). This paper objectively evaluates the denoising effect using peak signal-to-noise ratio (PSNR), which can be expressed as:  
\[\text{PSNR}=10\text{log}_{10}\bigg{[}\frac{(2^{n}-1)^{2}}{MSE}\bigg{]} \tag{17}\]  
where \(n\) is the bit-depth of the image, which is generally set to 8. \(MSE\) is the mean squared error between images.  
We compute the average PSNR results of processed reconstructed images across multiple datasets characterized by differing levels of noise under various network architectures. The comparison result of PSNR across various network architectures is shown in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **PSNR (dB)** \\ \hline QIS-SPFT without Anscombe, without IT & 28.214 \\ QIS-SPFT without Anscombe, with IT & 28.253 \\ QIS-SPFT with Anscombe, without IT & 28.221 \\ QIS-SPFT with Anscombe, with IT & 28.269 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Network structure verification and comparison results.  
The experimental results shows that the network incorporating the Anscombe transform and IT components has the best denoising performance. The introduction of the Anscombe transform plays a positive role in improving noise suppression performance. In photon-counting imaging, Poisson noise is more significant. This type of non-Gaussian noise makes the denoising process challenging. The Anscombe transform effectively alleviates the complexity of the noise distribution by converting Poisson noise into approximately Gaussian noise, reducing the modeling difficulty and improving noise suppression performance. This denoising structure has been proven to achieve better results in QIS denoising tasks [17]. If the Anscombe transform and its inverse process are not included, the neural network must autonomously learn this process through training, which is a relatively aggressive approach. Experimental results show that whether the IT component is included or not, the network configuration containing the Anscombe transform achieves slight improvements in PSNR, verifying the rationality and effectiveness of including the Anscombe transform in the network.  
Secondly, the IT component also significantly improves the denoising performance of the network. To further enhance denoising performance, the IT component--which comprises FCL, ReLU, T, and residual learning--extracts various features across layers. These features include both linear and nonlinear structural information, as well as significant structural details derived from inter-image pixel relationships. Experimental results indicate that the exclusion of the IT component results in a significant drop in PSNR, demonstrating that the IT component plays a crucial role in enhancing the network's denoising performance.  
When both the Anscombe transform and IT component are introduced simultaneously, the network achieves optimal performance. This indicates that the Anscombe transform and IT components are complementary within the network: the former effectively mitigates the complex noise composition problem in QIS, providing higher-quality input data for subsequent network processing, while the latter further exploits image correlation information between networks.