# Noise Suppressed Image Reconstruction for Quanta Image Sensors Based on Transformer Neural Networks
## 3 Method Description  
### Architecture of the Proposed QIS Reconstruction Method  
This paper introduces a neural network architecture named QIS-SPFT (QIS Serial-Parallel Fusion Transformer), which integrates both serial and parallel networks within Transformer frameworks to suppress Gaussian-Poisson noise in QIS reconstruction.  
The QIS-SPFT method capitalizes on the interaction of diverse structural information, obtained through attention mechanisms in both breadth and depth from various serial and parallel networks, to extract salient features for improved reconstruction of clean images. Its superior denoising performance is achieved through the Serial Module (SM) and Parallel Module (PM). The SM utilizes linear and nonlinear components to thoroughly search for essential information in image denoising. To gather more complementary information from different perspectives, the PM extensively explores interactions and cross-features between pixels obtained from two mixed networks, Subnet1 and Subnet2, thereby enhancing the network's adaptability to complex noise.  
The denoising framework QIS-SPFT use the Anscombe transformation, which makes the noise in jet-summation images closer to Gaussian distribution with constant variance. This variance-stabilizing technique facilitates the suppression of Poisson noise in QIS images. In this study, the neural network is incorporated as a denoiser within the QIS image reconstruction, and the neural network needs to learn to suppress the noise after Anscombe transformation. The architecture of the proposed QIS reconstruction method is shown in Figure 3.  
Within this network framework, a deep denoising network module is employed to thoroughly capture the structural information of images after variance stabilization. This module primarily comprises convolutional layers, activation functions, and Transformers. The convolutional layers convert the noisy images into linear features, the nonlinear activation functions extract richer features, while the Transformers discover the relationship between different image blocks, thus enhancing denoising performance in complex scenarios. Additionally, the framework integrates a robustness-enhancement network module, where two parallel sub-networks interact to extract complementary features from diverse perspectives, thereby improving the model's robustness and adaptability to various scenarios. To further enhance denoising performance, Transformers are embedded in both serial and parallel modules to extract more prominent features and effectively filter out noise. This network can be represented as:  
\[Resid^{-1}(I_{C})=RM(PM(SM(I_{N}))), \tag{8}\]  
where \(I_{N}\) represents the pre-reconstructed image, and \(SM\), \(PM\), and \(RM\) are defined as functions of the Serial Module, Parallel Module, and Residual Module. \(I_{C}\) is the clean image processed by the network. Further details about each module will be described in next subsection.  
To objectively assess the denoising performance of the proposed QIS-SPFT, the Mean Squared Error (MSE) is employed as the loss function for training the network parameters. Specifically, MSE is utilized to train the denoiser with paired training samples \(I_{C}^{i},I_{N}^{i}\) (\(1\leq i\leq n\)), where \(I_{C}^{i}\) and \(I_{N}^{i}\) denote the i-th clean and noisy images in the training dataset, respectively, and \(n\) represents the total number of training samples. This training process can be mathematically expressed as:  
Figure 3: Architecture of the proposed QIS reconstruction method.  
\[l(\theta)=\frac{1}{2n}\sum_{i=1}^{n}\left|\text{QIS-SPFT}(I_{N}^{i})-I_{C}^{i} \right|^{2}, \tag{9}\]  
where, \(l\) represents the loss function, and \(\theta\) denotes the parameters required for training QIS-SPFT.