In this paper, we introduce a total variation based variational model for denoising wrapped phase images. Our model improves on former methods by preserving discontinuities of the phase map and enforcing the fundamental Pythagorean trigonometric identity between the real and imaginary parts of the phase map enhancing the quality of the restored phase. The existence and uniqueness of the solution of our model is proven using standard methods. Further, we provide a fast fixed point method for finding the numerical solution and prove its convergence. Experiments on both synthetic and real patterns verify our findings.

翻译：本文提出了一种基于全变差的变分模型用于包裹相位图像的去噪。该模型通过保持相位图的非连续性，并强制相位图实部与虚部之间满足基本毕达哥拉斯三角恒等式，从而提升了恢复相位质量，改进了现有方法。我们采用标准方法证明了模型解的存在性与唯一性。此外，我们提出了一种快速不动点方法用于求解数值解，并证明了其收敛性。对合成模式与实际模式的实验均验证了我们的结论。