# LSTNet: A Reference-Based Learning Spectral Transformer Network for Spectral Super-Resolution
## 2 Related Work
### Spectral Super-Resolution  
Over the past few years, an increasing number of methods for SSR have been proposed, and CNN-based methods have achieved especially significant improvements over traditional methods, which often require prior knowledge assumptions to restrict the reconstruction task. [PERSON] et al. [19] have proposed a fast, low-cost method to recover a high-quality HSI directly from an MSI. Their approach uses a hyperspectral prior to create a sparse dictionary of spectral signatures and their corresponding MSI projections. Using the given spectral response function (SRF), a reconstructed HSI can be generated from an MSI through use of a sparse representation. [PERSON] et al. [20] have proposed a radial basis function, using \"white balancing\" as an intermediate step, for the reconstruction of a spectral reflectance image from a single MSI. This approach also brings the SRF into the model as a known term. [PERSON] et al. [21] have proposed a manifold learning method to recover an HSI from an MSI with a known SRF, with the assumption that the spectral information lies on an intrinsically low-dimensional manifold. However, most of these methods take the SRF as a known prior into the model, making the model highly dependent on this prior information. Furthermore, these traditional methods are pixel-level solving processes, which cannot be used for local and non-local spatial information.  
CNN-based SSR has gained increasing attention recently, due to its deep non-linear mapping and spatial information integration capabilities. [PERSON] et al. [22] first up-sampled MSIs in the spectral dimension through simple interpolation or compressive sensing measurements, and then used an end-to-end CNN-based network to recover the HSI from the up-sampled MSI. [PERSON] et al. [23] have proposed two strategies to reconstruct HSIs from MSIs. One is a deep residual network comprising a number of residual blocks; the other is an architecture that replaces the residual block with a dense block featuring a fusion scheme. [PERSON] et al. [24] introduced a modified UNet to learn multi-scale contextual information. [PERSON] et al. [25] proposed a pixel-aware deep function mixture network, composed of a function mixture block to determine the receptive field size and mapping function in a pixel-wise manner. [PERSON] et al. [26] proposed a novel adaptive weighted attention network with multiple dual residual attention blocks, which also utilizes the fact that the MSI can be projected by the reconstructed HSI using the known SRF to further enhance the constraints for more accurate reconstruction. [PERSON] et al. [27] proposed a deep hybrid 2D-3D CNN based on dual second-order attention with an SRF prior. [PERSON] et al. [28] proposed an intrinsic property guided end-to-end network consisting of a decomposition sub-network and a self-supervised sub-network. [PERSON] et al. [29] proposed a universal SSRnetwork based on physical optimization unfolding, enabling it to handle arbitrary MSIs, including single-resolution and cross-scale MSIs.  
The existing SSR methods mentioned above focus on the spectral reconstruction of an HSI using a single MSI as input, lacking further auxiliary spectral information to enhance the reconstruction accuracy of the spectrum. Attention mechanisms provide the possibility of using additional reference images to further promote spectral reconstruction.