# Multi-Scale CNN-Transformer Dual Network for Hyperspectral Compressive Snapshot Reconstruction
## 1 Introduction  
Hyperspectral imaging technology can capture the spectral information of real-world scenes within a specific wavelength range. Compared with three-channel visible RGB images, hyperspectral images usually have a wider spectral response range and a finer spectral sampling resolution. Each pixel represents spectral signatures of objects in the scene and can be used to better identify their categories. Therefore, hyperspectral images are widely used in various tasks, including ground object classification [1; 2; 3; 4], target detection and tracking, and change detection [2; 5]. In order to obtain complete spatial and spectral information, conventional hyperspectral imaging technology needs to scan in spectral or spatial dimensions. However, the scanning operation requires more imaging time and is not suitable for capturing dynamic scenes. Recently, a new hyperspectral imaging technology, called snapshot compressive imaging (SCI), has emerged; it is based on compressive sensing theory, which can significantly improve imaging efficiency. In these SCI systems, coded aperture snapshot spectral imaging (CASSI) is a potential solution. The CASSI system modulates incoming light through a coded aperture and accumulates the modulated light on a two-dimensional sensor array into a two-dimensional snapshot measurement duringa single exposure time. Then the 3D hyperspectral image (HSI) cube can be recovered from the 2D snapshot measurement during the reconstruction stage. The design of the reconstruction algorithm is the core issue of the CASSI system and a key factor affecting imaging quality. Traditional reconstruction methods [6; 7; 8; 9] recover the original hyperspectral image by solving optimization problems with prior regularization constraints. Some commonly used prior constraints include sparsity [10; 11; 12], total variation [8; 10; 13] and non-local similarity [9; 14; 15], etc. However, these handcrafted regularization constraints cannot adequately represent the spatial-spectral structure in hyperspectral images, which degrades the reconstruction quality. At the same time, the reconstruction procedure requires an iterative solution and the time complexity is high. In recent years, CNNs have been widely used in computer vision-related tasks due to their excellent capability of feature learning. They can adaptively learn the hierarchical feature representation of images in a data-driven way, and the learned features can be regarded as the deep prior of the underlying images. To this end, the researchers introduce CNN into the task of compressive snapshot imaging and guide the network to learn the end-to-end mapping from 2D snapshot measurements to 3D HSI. The CNN-based method has brought an effective improvement in reconstruction quality. However, due to the small receptive field of convolution kernels, CNN has certain limitations in capturing non-local self-similarity and long-range correlations in hyperspectral images. The Transformer is a new network structure that uses multi-head self-attention to model non-local correlations. It has received much attention in the field of computer vision and is used in image classification [16; 17; 18; 19; 20], target detection [21; 22; 23; 24], semantic segmentation, etc. Researchers have also proposed a Transformer-based network for compressive snapshot reconstruction. A representative Transformer-based reconstruction model (dubbed as MST) calculates self-similarity in the spectral dimension, effectively utilizing global similarity between spectral bands for reconstruction. MST [25] can achieve better reconstruction performance than the competing CNN. However, it has shortcomings in the representation of small-scale spatial structures, as the reconstructed images have the drawback of being over-smooth. A single CNN or Transformer structure cannot effectively represent the multi-scale spatial-spectral correlation of hyperspectral images.