Two-Dimensional Phase Unwrapping with Continuous Submodular Minimization

The phase unwrapping is recovering true phase from its 2π modulo observations which are related to some discrete optimization problems. The challenge is to exactly solve the discrete optimization problem arising from noisy data. In this paper, we propose a new continuous minimization method for phase unwrapping. Using the Lovász extension we transform the discrete problem to equivalent continuous problem. In contrast to conventional continuous minimization methods, our method can solve this discrete optimal problem exactly. In addition, one regularization term is added to the energy function to deal with noisy images. By using L1 norm for both data term and regularization term our method performs well for discontinuous images. Moreover, its implementation is very simple. A set of experiment results illustrates the effectiveness of the proposed method.