Simple phase unwrapping method with continuous convex minimization

Abstract

Phase unwrapping is a problem to reconstruct true phase values from modulo 2π phase values measured using various phase imaging techniques. This procedure is essentially formulated as a discrete optimization problem. However, most energy minimization methods using continuous optimization techniques have ignored the discrete nature and solved it as a continuous minimization problem directly, leading to losing exactness of the algorithms. We propose a new minimum norm method that can yield the optimal solution of the discrete problem by minimizing a continuous energy function. In contrast to the graph-cuts method, which is state of the art in this field, the proposed method requires much less memory space and a very simple implementation. Therefore, it can be simply extended to 3D or 4D phase unwrapping problems.