# Noise Suppressed Image Reconstruction for Quanta Image Sensors Based on Transformer Neural Networks
## 1 Introduction
Nevertheless, with the continued development of denoising technology, more complex neural network denoisers for QIS reconstruction need to be considered. In recent years, various filtering techniques have been developed to improve image denoising performance. Traditional methods, such as Gaussian smoothing, median filtering, and particularly Wiener filtering, have laid the groundwork for noise suppression by modeling local statistics and frequency domain characteristics. A comprehensive review of these approaches can be found in [20]. Building on these classical methods, filtering approaches based on doubly stochastic models have demonstrated strong potential in handling signal-dependent noise through adaptive probabilistic frameworks. For example, ref. [21] proposed an image restoration method using a doubly stochastic model, while [22] introduced a noise suppression approach that considers the two-layer stochastic nature of image acquisition. These methods provide important theoretical foundations for filtering  
Figure 1: Concept of spatio-temporal oversampling. under complex noise characteristics. With the rapid development of data-driven techniques, deep learning-based methods have also shown impressive results in recent years. These methods are capable of learning powerful priors directly from data and have demonstrated state-of-the-art performance in a wide range of denoising tasks. A recent survey by [23] provides a comprehensive overview of the progress in this area. The unique hardware characteristics of QIS inherently provide superior capability for low-light imaging. By leveraging high-speed frame acquisition and high temporal oversampling rate, QIS can achieve imaging even in extremely low-light conditions. However, this comes at the cost of longer imaging time and significantly increased data volume. More specifically, we contribute to the literature of QIS image reconstruction as follows:  
* This study propose a reconstruction method that suppress photon shot noise during the QIS imaging process under a practical and acceptable temporal oversampling rate based on deep neural network instead of traditional denoising. * The proposed neural network framework integrates CNN and Transformer to improve denoising performance. A hybrid structure combining serial and parallel is introduced in the network framework to enhance the strength and robustness of denoising. The serial module deeply explores the key information in image denoising, while the parallel module widely explores more relevant and complementary information between pixels from different angles, thereby enhancing the adaptability of the QIS-SPFT denoiser to complex scenes. In the network, a variance-stabilizing transformation is used to convert the high Poisson noise in QIS into Gaussian noise to enhance the performance as well. The remainder of the paper is organized as follows. Section 3 introduces the background of QIS imaging. Section 4 provides a detailed theoretical analysis of the proposed image reconstruction method. Section 5 presents and compares experimental results. Finally, Section 6 concludes the paper.