Phys-HUSPU: a physics-constrained and heteroscedastic uncertainty-guided phase unwrapping framework

Phase unwrapping is a critical step in optical metrology and imaging. Existing deep learning methods predominantly rely on supervised learning and are trained on large-scale simulated data. Such methods essentially fit the statistical distribution of the training set rather than learning physical mechanisms. When facing non-ideal scenarios such as phase aliasing and overexposure, networks lacking physical constraints exhibit limited generalization capability. To address this, we propose Phys-HUSPU, a physics-constrained and heteroscedastic uncertainty-guided phase unwrapping framework. This method reduces the dependence on ground-truth labels by using physics-informed penalty and regularization terms to guide the solution space. The network reconstructs phase unwrapping as a joint regression problem of wrap-count gradient fields and pixel-wise heteroscedastic uncertainty. The predicted uncertainty serves as adaptive weights: imposing gradient-domain data fidelity constraints in reliable data regions while adaptively enhancing physical priors in unreliable regions, thereby effectively constraining the solution space and inferring physically consistent phase solutions. Experimental results demonstrate that this framework significantly improves network robustness in non-ideal scenarios such as noise interference, phase aliasing, and signal truncation and demonstrates excellent generalization in cross-domain applications.