In contrast to the well-investigated field of SAR-to-Optical translation, this study explores the lesser-investigated domain of Optical-to-SAR translation, a challenging field due to the ill-posed nature of this translation. The complexity arises as a single optical data can have multiple SAR representations based on the SAR viewing geometry. We propose a novel approach, termed SAR Temporal Shifting, which inputs an optical data from the desired timestamp along with a SAR data from a different temporal point but with a consistent viewing geometry as the expected SAR data, both complemented with a change map of optical data during the intervening period. This model modifies the SAR data based on the changes observed in optical data to generate the SAR data for the desired timestamp. Our model, a dual conditional Generative Adversarial Network (GAN), named Temporal Shifting GAN (TSGAN), incorporates a siamese encoder in both the Generator and the Discriminator. To prevent the model from overfitting on the input SAR data, we employed a change weighted loss function. Our approach surpasses traditional translation methods by eliminating the GAN's fiction phenomenon, particularly in unchanged regions, resulting in higher SSIM and PSNR in these areas. Additionally, modifications to the Pix2Pix architecture and the inclusion of attention mechanisms have enhanced the model's performance on all regions of the data. This research paves the way for leveraging legacy optical datasets, the most abundant and longstanding source of Earth imagery data, extending their use to SAR domains and temporal analyses. To foster further research, we provide the code, datasets used in our study, and a framework for generating paired SAR-Optical datasets for new regions of interest. These resources are available on github.com/moienr/TemporalGAN
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