# LSTNet: A Reference-Based Learning Spectral Transformer Network for Spectral Super-Resolution
## 4 Experiments and Results
### Experimental Data Sets and Setting  
**Simulation data**. Several widely used HSI data sets were used as simulation data for this experiment. These are the Pavia University data, Pavia Centre data, and University of Houston data. The Pavia University data were acquired by an ROSIS-3 airborne sensor in 2003. These data have the size of 610 \(\times\) 340 pixels and consist of 115 bands. Due to the effects of noise and water vapor absorption, 12 bands were removed. The ground sample distance (GSD) of these data was 1.3 m, and the spectral range covers 430 to 840 nm. The Pavia Centre data were also acquired by an ROSIS-3 sensor, with a size of 1096 \(\times\) 1096 pixels and consisting of 102 bands after removing the water vapor absorption bands. To test the performance of the spectral transformer, the Pavia Centre data were used as reference imagery and Pavia University data were used as the input imagery. As shown in Figure 4, we divided the images into two parts for training and testing. Each part of the Pavia Centre data consisted of 548 \(\times\) 1096 pixels, and each part of the Pavia University data consisted of 305 \(\times\) 340 pixels. To simulate MSI, the blue-SWIR1 SRF of Landsat 8 was used to simulate MSIs from HSIs for all the images. Figure 4: Original Pavia Centre and Pavia University data sets: (**a**) Pavia Centre; (**b**) Pavia University. The border color indicates the purpose of the image. The University of Houston data were acquired by an ITRES CASI 1500 sensor over the University of Houston campus and its neighborhood on 16 February 2017. The original data have the size of 1202 \(\times\) 4172 pixels at a 1 m GSD, with 48 bands covering the 380-1050 nm spectral range. These data were provided for the 2018 IEEE GRSS data fusion contest. To verify the proposed reference-based transformer, we split these data into several pieces, where the size of each piece was 601 \(\times\) 596 pixels, as shown in Figure 5. To simulate MSI, the blue-SWIR1 SRF of Landsat 8 was used to simulate MSIs from HSIs for all the pieces. **Real data. ** For this study, we also verified the proposed method on real data, for which Sentinel-2 and GF5 data were used. The GF5 data were acquired by the GF5-Advanced Hyperspectral Imager (AHSI) on 10 November 2019 over Xuchang city, Henan province, China. It has the size of 2083 \(\times\) 2008 pixels, with 330 bands covering the spectral range 390-2500 nm and 30 m GSD. The Sentinel-2 data were acquired on 14 November 2019. We used ENVI to select the same region as the GF5 data. After image registration, each image was divided into four parts, as shown in Figure 6.  
**Experimental environment. ** The proposed method was implemented using the PyTorch framework [44] and trained using the Adam optimizer, which was set to its default  
Figure 5: The original University of Houston data set was separated into many pieces, each with size of 601 \(\times\) 596 pixels. The border color indicates the purpose of the image. Figure 6: Illustration of Sentinel-2 and GF5 data sets, (**a**) is the Sentinel-2 dataset, (**b**) is the GF-5 dataset. parameters [45]. The initial learning rate was set to \(3\times 10^{-4}\), with linear stepping decay set from epochs 500 to 2000. The parameters of the network were initialized using the Kaiming initialization method. We used randomly selected patches to train the network, and the patch size was set to 64 \(\times\) 64. In the SRM, eight RDCA blocks were stacked for each backbone sub-network, and the number of features for each convolutional layer was set to 128, except for the initial convolutional layer and the last convolutional layer related to input and output bands. The training environment consisted of an Intel i-7 6850K CPU, 128 GB RAM, and \(4\times\) GTX 1080 Ti. **Quality assessment.