Itoh-Constrained Hybrid Graph Learning With Sparse Supervision for InSAR Phase Unwrapping

Abstract

Phase unwrapping (PU) is a fundamental step in synthetic aperture radar interferometry (InSAR), yet it remains an inherently ill-posed problem due to the $\text{2}\pi$ ambiguity of the interferometric phase. Existing deep learning-based PU methods typically rely on dense pixelwise supervision using absolute phase values, which introduces a fundamental mismatch with the intrinsic structure of PU and often leads to poor generalization. In particular, the mapping from wrapped phase to absolute phase is inherently one-to-many, making pixelwise regression ambiguous and difficult to learn. In contrast, classical PU methods mitigate the ill-posedness by exploiting the Itoh condition, which enforces consistency on phase differences rather than absolute values. This observation suggests that effective supervision for PU should be imposed on phase gradients, i.e., along edges. To this end, we propose an Itoh-constrained hybrid graph (IC-HG) framework, which reformulates PU as an edgewise gradient regression problem using sparse observations. By enforcing the Itoh condition on graph edges, the proposed method ensures physically consistent phase differences and alleviates the ill-posedness of PU. Specifically, IC-HG constructs a weighted hybrid graph, where a global minimum spanning tree guarantees global connectivity and suppresses phase drift, while dynamically sampled local K-nearest neighbor edges capture fine-scale phase variations and prevent geometric overfitting. Extensive experiments demonstrate that the proposed method consistently outperforms dense supervision and other baseline methods under both uniform and nonuniform sampling conditions. Moreover, IC-HG exhibits strong robustness and generalization capability, particularly when only sparse supervision is available, highlighting its effectiveness for real-world InSAR applications.