Two-dimensional Phase Unwrapping with Priori Boundary Condition

Phase unwrapping is essential for many applications such as Interferometric synthetic aperture radar, MRI, and X-ray phase imaging etc. In these applications, the phase is determined only in the principal value range of [-π,π). The unwrapping that recover true phase method becomes difficult when the measured object possesses big discontinuity. In these minimum norm methods, for unwrapping, it is needed to minimize the difference between the gradient of the wrapped phase and that of the unwrapped phase using the Lp norm. Many authors suggest that the goal of phase unwrapping should be minimizing the Lo norm problem. However, previous methods have reached its limits as this is a nonconvex problem. To solve this difficulty, in this paper we used boundary information as the priori condition which is suitable in many applications. Then the unwrapped phase is given by solving a Lp (p ≥ 1) norm minimization problem that belongs to convex optimization. The simulation results demonstrate that our method is effective.