# Noise Suppressed Image Reconstruction for Quanta Image Sensors Based on Transformer Neural Networks
## 3 Method Description
### Detail of the QIS-SPFT Denoiser
\begin{split} O_{PM}&=PM(O_{SM})\\ &=O_{Subnet1}\\ &=Subnet1(O_{SM},O_{Subnet2}),\end{split}  \tag{13}\]  
where \(O_{PM}\) is the output of the parallel module, and \(O_{Subnet2}\) is the output of subnetwork 2. In the parallel module, subnetwork 2 can be expressed by Equation (14). \[ \begin{split} O_{Subnet2}&=Subnet2(O_{SM})\\ &=T(C(CR(T(C(CR(O_{SM}))+O_{SM}))))\\ &+T(C(CR(O_{SM}))+O_{SM})),\end{split}  \tag{14}\]  
Subnetwork 1 can be expressed by Equation (15). \[ \begin{split} O_{Subnet1}&=Subnet1(O_{SM},O_{ Subnet2})\\ &=IT(T(CR(C(Concat(T(T(\\ & CR(O_{SM})))),O_{Subnet2}))))),\end{split}  \tag{15}\]The SM deeply searches for key information in image denoising, while the PM extensively explores more relevant and complementary information between pixels from different perspectives to enhance the adaptability of the QIS-SPFT denoiser to complex scenes. Its effectiveness is achieved through the interaction of two heterogeneous networks, namely subnetwork 1 and subnetwork 2, at multiple feature levels. These two subnetworks interact and acquire complementary features from different perspectives to enhance the robustness of the obtained denoising model. The \(Conv+R\) component is used to extract nonlinear information, while the \(Conv\) component is used to extract linear information. The \(T\) component functions between \(Conv\) and \(Conv+R\) to extract salient information. Furthermore, to augment the denoising network's capability, the input of \(Conv+R\) and the output of \(Conv\) are integrated using a residual learning operation. In the parallel module (PM), two robustness enhancement operations are employed. The first operation aims to improve the robustness of the features obtained from the denoiser by introducing an interaction mechanism between subnetwork 1 and subnetwork 2, namely the merging operation Concat. The Concat operation includes depthwise separable convolution layers, enabling information sharing and mutual influence between the two subnetworks, thereby enhancing the module's robustness against noise. Here, robustness refers to the module's ability to maintain effective denoising performance when facing different types of noise or complex noise conditions. The second operation, following the information interaction between different subnetworks, incorporates an improved Transformer component, \(IT\), to eliminate interference information from previous interactions. The \(IT\) component consists of the stacks \(FCL\), \(T\), \(FCL+R\), and \(FCL\). Additionally, to enhance information acquisition, residual learning operations are conducted between the input of \(IT\) and the output of \(FCL\), as well as between the outputs of \(T\) and \(FCL\). The residual module (RM) consists of a convolutional layer and a residual learning operation, aiming to construct a clean image by performing residual learning between the original noisy image and the predicted image in QIS-SPFT. The original image in this module is the noisy image before the Anscombe transformation, while the predicted image is the one obtained after the inverse Anscombe transformation. The convolution kernel size in this module is \(3\times 3\), with 64 input channels and 1 output channel. RM can be expressed by Equation (16). Figure 5: Detail of the parallel module. \[ \begin{array}{ll}l_{c}&=RM(O_{PM})\\ &=I_{N}-C(O_{PM}).\end{array}  \tag{16}\]