Fusion and Super-Resolution of Remote Sensing Images Using Deep Learning and Gram-Schmidt Orthogonalization

Authors

  • Sin-Gil Kim Department of Information Science, University of Sciences, Unjong District, Pyongyang, Democratic People’s Republic of Korea
  • Il-Kwang Jo Institute of Earth Environmental Geoinformatics, Unjong District, Pyongyang, Democratic People’s Republic of Korea
  • Gyong-Song Chae Institute of Earth Environmental Geoinformatics, Unjong District, Pyongyang, Democratic People’s Republic of Korea
  • Ji-Chon Ro Institute of Earth Environmental Geoinformatics, Unjong District, Pyongyang, Democratic People’s Republic of Korea

DOI:

https://doi.org/10.52562/injoes.2026.1632

Keywords:

Sentinel-2, pan-sharpening, convolutional neural network, aerial imagery, urban vegetation

Abstract

Multispectral satellite images contain rich spectral information but often have low spatial resolution. Super-resolution of these images is important for resource development, environmental protection, disaster prevention, regional ecology, and change detection. Deep learning models, including convolutional neural networks (CNNs), have been widely applied to the super-resolution of satellite images, including Sentinel-2 images. However, their output cannot exceed the maximum spatial resolution of the sensor. Here, we propose a method that first enhances the 20 m Sentinel-2 bands to 10 m using a CNN and then fuses them with 1 m aerial images by Gram-Schmidt orthogonal transformation and its inverse, while preserving multispectral information. The method was tested on the fusion of aerial and Sentinel-2 images to visualize vegetation distribution in urban areas. The proposed network achieved a root mean square error (RMSE) of 43.5 and a correlation coefficient (CC) of 0.941, compared with 123.4 and 0.811 for bicubic interpolation and 117.8 and 0.866 for area-to-point regression kriging (ATPRK). The fused images appeared as sharp as the aerial images while preserving the shape of the original spectral curves.

Downloads

Download data is not yet available.

References

Aiazzi, B., Baronti, S., & Selva, M. (2007). Improving component substitution pansharpening through multivariate regression of MS + Pan data. IEEE Transactions on Geoscience and Remote Sensing, 45(10), 3230-3239. https://doi.org/10.1109/TGRS.2007.901007

Björck, Å. (1967). Solving linear least squares problems by Gram-Schmidt orthogonalization. BIT, 7(1), 1–21. https://doi.org/10.1007/BF01934122

Cai, D., & Zhang, P. (2022). T3SR: Texture transfer transformer for remote sensing image superresolution. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 15, 7346–7358. https://doi.org/10.1109/jstars.2022.3198557

Dong, X., Xi, Z., Sun, X., & Gao, L. (2019). Transferred multi-perception attention networks for remote sensing image super-resolution. Remote Sensing, 11(23), Article 2857. https://doi.org/10.3390/rs11232857

Drusch, M., Del Bello, U., Carlier, S., Colin, O., Fernandez, V., Gascon, F., ... & Bargellini, P. (2012). Sentinel-2: ESA's optical high-resolution mission for GMES operational services. Remote sensing of Environment, 120, 25-36. https://doi.org/10.1016/j.rse.2011.11.026

Gargiulo, M., Mazza, A., Gaetano, R., Ruello, G., & Scarpa, G. (2019). Fast super-resolution of 20 m Sentinel-2 bands using convolutional neural networks. Remote Sensing, 11(22), Article 2635. https://doi.org/10.3390/rs11222635

Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980. https://doi.org/10.48550/arXiv.1412.6980

Lanaras, C., Bioucas-Dias, J., Galliani, S., Baltsavias, E., & Schindler, K. (2018). Super-resolution of Sentinel-2 images: Learning a globally applicable deep neural network. ISPRS Journal of Photogrammetry and Remote Sensing, 146, 305–319. https://doi.org/10.1016/j.isprsjprs.2018.09.018

Lei, S., Shi, Z., & Mo, W. (2022). Transformer-based multistage enhancement for remote sensing image super-resolution. IEEE Transactions on Geoscience and Remote Sensing, 60, Article 5615611. https://doi.org/10.1109/tgrs.2021.3136190

Lu, T., Wang, J., Zhang, Y., Wang, Z., & Jiang, J. (2019). Satellite image super-resolution via multi-scale residual deep neural network. Remote Sensing, 11(13), Article 1588. https://doi.org/10.3390/rs11131588

Ma, W., Pan, Z., Yuan, F., & Lei, B. (2019). Super-resolution of remote sensing images via a dense residual generative adversarial network. Remote Sensing, 11(21), Article 2578. https://doi.org/10.3390/rs11212578

Romero, L. S., Marcello, J., & Vilaplana, V. (2020). Super-resolution of Sentinel-2 imagery using generative adversarial networks. Remote Sensing, 12(15), Article 2424. https://doi.org/10.3390/rs12152424

Vivone, G., Alparone, L., Chanussot, J., Dalla Mura, M., Garzelli, A., Licciardi, G. A., ... & Wald, L. (2014). A critical comparison among pansharpening algorithms. IEEE Transactions on Geoscience and Remote Sensing, 53(5), 2565-2586. https://doi.org/10.1109/TGRS.2014.2361734

Wang, Y., Shao, Z., Lu, T., Huang, X., Wang, J., Chen, X., Huang, H., & Zuo, X. (2023). Remote sensing image super-resolution via multi-scale texture transfer network. Remote Sensing, 15(23), Article 5503. https://doi.org/10.3390/rs15235503

Wang, Q., Shi, W., Li, Z., & Atkinson, P. M. (2016). Fusion of Sentinel-2 images. Remote sensing of environment, 187, 241-252. https://doi.org/10.1016/j.rse.2016.10.030

Xiong, Y., Guo, S., Chen, J., Deng, X., Sun, L., Zheng, X., & Xu, W. (2020). Improved SRGAN for remote sensing image super-resolution across locations and sensors. Remote Sensing, 12(8), Article 1263. https://doi.org/10.3390/rs12081263

Downloads

Published

2026-03-05

How to Cite

Fusion and Super-Resolution of Remote Sensing Images Using Deep Learning and Gram-Schmidt Orthogonalization. (2026). Indonesian Journal of Earth Sciences, 6(1), A1632. https://doi.org/10.52562/injoes.2026.1632

Similar Articles

1-10 of 39

You may also start an advanced similarity search for this article.