PSSformer: Permanent Scatterers Selection Method for SAR Interferometry based on Temporo-Spatial Vision Transformers

Multi-temporal synthetic aperture radar interferometry (SAR, MT-InSAR) has been widely recognized as an effective technique for monitoring surface deformation and marking a significant advancement in satellite geodesy to millimeter-level precision. As one of the most representative MT-InSAR methods, permanent scatterer interferometry (PS, PSI) focuses on the most elite pixels over the temporal and spatial scales of SAR images. The selection of PS points is the cornerstone of the excellent performance of PSI, directly influencing the accuracy and density of surface deformation products. Most traditional methods use thresholds to divide PS and non-PS pixels, and their results will no longer be accurate when the surface deformation patterns deviate from the prior model. Benefiting from the development of deep learning, data-driven methods have been widely proposed in recent years and exhibit superior efficiency. However, existing approaches do not fully exploit the contextual relationships between phase, amplitude, time, and spatial dimensions. This will result in the selected PS points showing representative only in certain dimensions.

Therefore, this paper proposed a novel deep learning method for PS selection that leverages the temporo-spatial context features of amplitude images and interferometric phase. Specifically, a pseudo-Siamese temporo-spatial vision transformer (ViT) architecture is employed to process input amplitude and phase time-series stacks simultaneously. In the backbone, the positional information is incorporated into the image tokens via the temporal and spatial embedding layers, and the local features in the context of the time series images are derived by the temporal and spatial encoder. Through a feature fusion module, multi-scale features from amplitude and phase are synergistically integrated. Then, it is output to the decoding head, and the high-quality PS points are predicted pixel by pixel through a multilayer perceptron.

The proposed model was trained on a dataset containing time-series SAR amplitude images and interferometric phase stacks of Barcelona, acquired by the TerraSAR between 2009 and 2011. The dataset includes 8,689 samples for training and 965 samples for validation, with data pre-processing and PS annotation performed using the SUBSIDENCE software from the Universitat Politècnica de Catalunya. To address the class imbalance between PS and non-PS points, the focal loss function was employed. The proposed model was evaluated using metrics like intersection over union (IoU), F1-score, precision, and recall. PS points selected by our method are validated via qualitative and quantitative comparisons against other state-of-the-art methods.

Experimental results indicate that the proposed method markedly improves the density, precision, and phase integrity of PS points. Compared to traditional methods, the proposed model yields more complete and continuous PS point details on buildings and man-made infrastructure, reduces false points, and improves computational efficiency. Additionally, the proposed method performs robustly across diverse land types and is extendable to distributed scatterer (DS) pixel selection. All model codes and training configurations will be available at https://dagshub.com/zhangyfcsu/pssformer.