A variational approach to one dimensional phase unwrapping

Over the past ten years, many phase unwrapping algorithms have been developed and formulated in a discrete setting. Here we propose a variational formulation to solve the problem. This continuous framework will allow us to impose some constraints on the smoothness of the solution and to implement them efficiently. This method is presented in the one dimensional case, and will serve as a basis for future developments in the real 2D case. Numerical schemes and results on a synthetic noisy wrapped signal are given.