BB-PIP-U²Net: a physics-constrained optimization framework for robust multibaseline InSAR phase unwrapping

Noise interference critically limits phase unwrapping (PU) performance in multi-baseline (MB) InSAR. This study proposes BB-PIP-U²Net, a physics-constrained hybrid framework integrating deep learning with branch-and-bound pure integer programming (BB-PIP). We first construct a physics-realistic dual-simulation integrated (PRDS) dataset with 10,703 samples. Zernike polynomials are used to model phase noise, improving terrain authenticity. Within the U² structure, depthwise separable convolutions (DSConv) reduce computational redundancy, while a hybrid attention (HA) mechanism suppresses noise and enhances fringe recognition. Crucially, the BB-PIP module serves as a mathematically traceable optimization layer. By using the bottleneck latent features as a "warm start," it transforms the prediction into a constrained global integer optimization problem, providing physical interpretability to the unwrapping process and ensuring mathematical optimality. Experimental results demonstrate that BB-PIP- U²Net is highly robust to noise. Under high-noise conditions (3 dB SNR), the proposed method achieves an RMSE of 1.18 rad, which is significantly lower than that of PIPNet (1.58 rad) and the traditional TSPA (3.66 rad). Processing speed remains 5.8% faster than that of PIPNet. Validations on real SAR data demonstrate that BB-PIP- U²Net provides a balance between computational efficiency and unwrapping accuracy. The results have significant implications for improving measurement accuracy and deformation monitoring in InSAR technology.