Phase Unwrapping Algorithm for Large-Gradient Subsidence Funnels in Mining Areas Based on Target Detection and Gaussian Modeling

Objectives Most phase unwrapping algorithms in interferometric synthetic aperture radar （InSAR)technology rely on the assumption of phase continuity. However, mining subsidence is characterized by its small spatial extent, large-gradient subsidence, and sudden occurrences, which result in dense interference fringes in the interferograms, making it difficult to satisfy the phase continuity assumption.

Methods To address this challenge, we propose a phase unwrapping method that combines a deep learning-based object detection network with subsidence funnel inversion modeling. The goal is to identify and simulate subsidence funnels in the interferograms, reducing the phase gradient within the wrapped phase and thereby achieving high-precision phase unwrapping. The method first utilizes simulated and real-world interferograms from mining areas to train a subsidence funnel detection model within the YOLOv10 framework, enabling automatic large-scale identification of subsidence funnels in interferograms. Then, a two-dimensional Gaussian model, optimized using a minimum angular deviation objective function, is employed to invert and model each subsidence funnel. The modeled phase is subtracted from the interferogram, and the residual phase is filtered to reduce phase aliasing caused by filtering and to increase the signal-to-noise ratio of the interferogram. Finally, the filtered residual phase is unwrapped and added back to the modeled phase to restore the true unwrapped phase.

Results Using simulated data and the Lutan-1 dataset covering the Datong region in Shanxi, China, the proposed method was analyzed in terms of phase residual points before and after unwrapping, along with statistical results from the simulated data. Compared to traditional unwrapping methods used in mining areas, the proposed method demonstrates stronger robustness and higher accuracy. In nonlinear high-gradient deformation areas, the mean squared error was reduced by 57.4%, and the average number of residual points decreased by 23.4%.

Conclusions By combining model identification with fringe reduction, the wrapped phase better satisfies the phase continuity assumption, reducing the impact of large gradient deformations on subsequent unwrapping operations and improving the accuracy of the unwrapped results. Notably, the proposed algorithm can better restore the true phase at the center of subsidence funnels, a task that traditional two-dimensional unwrapping algorithms struggle to achieve.