Path-independent phase unwrapping using phase gradient and total-variation (TV) denoising

Phase unwrapping is a challenging task for interferometry based techniques in the presence of noise. The majority of existing phase unwrapping techniques are path-following methods, which explicitly or implicitly define an intelligent path and integrate phase difference along the path to mitigate the effect of erroneous pixels. In this paper, a path-independent unwrapping method is proposed where the unwrapped phase gradient is determined from the wrapped phase and subsequently denoised by a TV minimization based method. Unlike the wrapped phase map where 2π phase jumps are present, the gradient of the unwrapped phase map is smooth and slowly-varying at noise-free areas. On the other hand, the noise is greatly amplified by the differentiation process, which makes it easier to separate from the smooth phase gradient. Thus an approximate unwrapped phase can be obtained by integrating the denoised phase gradient. The final unwrapped phase map is subsequently determined by adding the first few modes of the unwrapped phase. The proposed method is most suitable for unwrapping phase maps without abrupt phase changes. Its capability has been demonstrated both numerically and by experimental data from shearography and electronic speckle pattern interferometry (ESPI).