Two-dimensional phase unwrapping based on U2-Net in complex noise environment

This paper proposes applying the nested U2-Net to a two-dimensional phase unwrapping (PU). PU has been a classic well-posed problem since conventional PU methods are always limited by the Itoh condition. Numerous studies conducted in recent years have discovered that data-driven deep learning techniques can overcome the Itoh constraint and significantly enhance PU performance. However, most deep learning methods have been tested only on Gaussian white noise in a single environment, ignoring the more widespread scattered noise in real phases. The difference in the unwrapping performance of deep network models with different strategies under the interference of different kinds of noise or drastic phase changes is still unknown. This study compares and tests the unwrapping performance of U-Net, DLPU-Net, VUR-Net, PU-GAN, U2-Net, and U2-Netp under the interference of additive Gaussian white noise and multiplicative speckle noise by simulating the complex noise environment in the real samples. It is discovered that the U2-Net composed of U-like residual blocks performs stronger anti-noise performance and structural stability. Meanwhile, the wrapped phase of different heights in a high-level noise environment was trained and tested, and the network model was qualitatively evaluated from three perspectives: the number of model parameters, the amount of floating-point operations, and the speed of PU. Finally, 421 real-phase images were also tested for comparison, including dynamic candle flames, different arrangements of pits, different shapes of grooves, and different shapes of tables. The PU results of all models are quantitatively evaluated by three evaluation metrics (MSE, PSNR, and SSIM). The experimental results demonstrate that U2-Net and the lightweight U2-Netp proposed in this work have higher accuracy, stronger anti-noise performance, and better generalization ability.