## 3 Experimental Results
### Experiment Design and Evaluation  
Three traditional STF methods (STARFM [13], FSDAF [11], and Fit-FC [15]) and five deep learning-based methods (EDCSTFN [21], GAN-STFM [22], MLFF-GAN [23], STF-Trans [28], and CTSTFM [29]) are used for comparison with the proposed method. All the mentioned approaches rely solely on a pair of reference images captured at different time points. These methods can be grouped based on their focus on either temporal change capture or spatial detail enhancement. STARFM, Fit-FC, EDCSTFN, and MLFF-GAN primarily target temporal difference modeling, leveraging input data from different time points to extract and reconstruct temporal features. On the other hand, GAN-STFM, STF-Trans, and CTSTFM emphasize spatial detail enhancement, using advanced architectures to generate high-resolution outputs by refining spatial features. FSDAF integrates temporal difference modeling and spatial detail enhancement by using linear unmixing theory to capture class changes between two time points and employing thin-plate spline interpolation for spatial prediction. The datasets are divided into training and testing sets. For the CIA dataset, all MODIS-Landsat image pairs, except those from 25 November 2001, 12 January 2002, and 22 February 2002, are included in the training set. During testing, the image pair from 25 November 2001 and the coarse image from 12 January 2002 are used to predict the fine image for 12 January 2002. Similarly, for the LGC dataset, all images except those from 26 November 2004,12 December 2004, and 28 December 2004, are included in the training data. For testing, the image pair from 26 November 2004 and the coarse image from 12 December 2004 are used to predict the fine image for 12 December 2004. In the Wuhan dataset, all image pairs except those from 18 October 2015 and 30 October 2017 are allocated for training. For testing, 30 October 2017 is considered the reference time, while 18 October 2015 serves as the prediction time. A uniform training set generation method is employed for all DL approaches. For the CIA and LGC datasets, MODIS-Landsat image pairs from different dates are randomly selected as reference images for each predicted time [22; 26]. The images are cropped to a size of 256 \(\times\) 256 with a stride of 200. For the Wuhan dataset, the reference-prediction time pairing method provided by the data provider is used. Given the relatively smaller dataset size, the cropping size is maintained at 256 \(\times\) 256, but the stride is reduced to 125. This process yields 1260 training samples from the CIA dataset, 2464 training samples from the LGC dataset, and 637 training samples from the Wuhan dataset. During the testing phase, no cropping is performed, and the original image size is used as input. STF-Trans, CTSTFM, and BCSR-STF all incorporate the self-attention mechanism from Transformers. In STF-Trans, the embedding dimension is set to 512, while CTSTFM uses an embedding dimension of 64. For BCSR-STF, due to its pyramid structure, the embedding dimensions are configured as (48, 96, 192, 192) across different levels. For BCSR-STF, the initial learning rate is 2 \(\times\) 10\({}^{-4}\). All deep learning-based methods are trained on one NVIDIA RTX 3090 GPU using the data enhancement strategy of image random flip or rotation and the training strategy of starting from scratch; no other tricks are used. To comprehensively evaluate the performance of BCSR-STF, both quantitative and qualitative metrics are employed. (1) Quantitative metrics: Six evaluation metrics are used [26]: Root Mean Square Error (RMSE), Structure Similarity Index (SSIM), Universal Image Quality Index (UIQI), Correlation Coefficient (CC), Spectral Angle Mapper (SAM), and Erreur Relative Global Adimensionnelle de Synthene (ERGAS). Lower values of RMSE, SAM, and ERGAS, alongside higher values of SSIM, UIQI, and CC, signify a more reliable and accurate fusion outcome. These metrics comprehensively assess error, structural fidelity, spectral consistency, and overall synthesis quality of the fused images.