# Transformer-Based Cascading Reconstruction Network for Video Snapshot Compressive Imaging
## 1 Introduction  
Signal sampling is the first prerequisite for signal processing and analysis. The compressive sensing theory [1; 2; 3; 4; 5] points out that sparse signals or signal sparse in the transform domain can be recovered from much less compressed measurements than the Nyquist sampling. It is a more efficient signal sensing method, which can realize the synchronous compression of signals during the sampling process. In recent years, a variety of new computational imaging methods based on compressive sensing theory have emerged [6; 7]. The Coded Aperture Compressive Temporal Image (CACTI) is one of the representative methods. As shown in Figure 1, this imaging mode first modulates the video scene (image sequence) through different masks and then integrates and accumulates along the time dimension to form a single-frame snapshot measurement, which is finally captured by a two-dimensional detector. Video snapshot compressive imaging modulates and compresses the video sequences in the time dimension, which canreduce the burden of data storage and the requirements of the transmission bandwidth. Since the snapshot measurement is encoded and compressed information, it is necessary to design an efficient reconstruction algorithm to recover the original video, which is an important factor affecting the quality of video snapshot compressive imaging. The existing reconstruction algorithms are mainly divided into two categories: iterative optimization-based methods and deep network-based methods. The iterative optimization methods [8; 9; 10; 11; 12; 13; 14] formulate the reconstruction process as a variational problem with a priori regularization constraints and solve it through the optimization algorithm iteratively. Total variation, the Gaussian mixture model and non-local low rank are widely used prior regularization constraints. However, these hand-crafted models cannot represent complex and dynamic scene content in videos effectively, which degrades the reconstruction quality. At the same time, this category of methods involves multiple iterations, and each iteration needs to solve the proximal operator of the priori regularization constraint [13], which has a high computational complexity and long reconstruction time. For example, the DeSCI method [8] used nonlocal low rank as a priori to improve the reconstruction quality, but it takes about \(1\) h to recover eight frames from the measurement. Inspired by the successful application of the deep network model in computer vision tasks, scholars have also applied the deep network to snapshot compressive imaging tasks [15; 16; 17; 18; 19; 20; 21]. Their main idea is to design a network to directly learn the inverse mapping from the snapshot measurement to the original signal. Unlike the iterative optimization solution, the original video can be quickly reconstructed without iteration by inputting the snapshot measurement into the trained reconstruction networks. At present, the mainstream reconstruction networks mainly use the convolution neural network to extract features for reconstruction. However, the size of the convolution kernel is usually small, so they can only extract local features. Although stacking multiple convolutions can improve the receptive field range of deep features, it still cannot capture the long-range spatiotemporal correlation in image sequences, affecting the reconstruction quality. How to represent the video dynamic scene content effectively, especially how to make use of long-range spatiotemporal correlation, is the key to improving the reconstruction quality. Transformer [22; 23; 24; 25; 26; 27; 28; 29; 30], as a novel network architecture, uses a self-attention mechanism to represent long-term relations and has shown excellent performance in visual tasks. Therefore, we introduce Transformer into the task of video snapshot compressive imaging and propose a Transformer-based Cascading Reconstruction Network.