Bioucas-Dias José M, Valadão Gonçalo
Instituto de Telecomunicações, Instituto Superior Técnico, and the Technical University of Lisbon, 1049-001 Lisboa, Portugal.
IEEE Trans Image Process. 2007 Mar;16(3):698-709. doi: 10.1109/tip.2006.888351.
Phase unwrapping is the inference of absolute phase from modulo-2pi phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are first-order Markov random fields. We provide an exact energy minimization algorithm, whenever the corresponding clique potentials are convex, namely for the phase unwrapping classical Lp norm, with p > or = 1. Its complexity is KT (n, 3n), where K is the length of the absolute phase domain measured in 2pi units and T (n, m) is the complexity of a max-flow computation in a graph with n nodes and m edges. For nonconvex clique potentials, often used owing to their discontinuity preserving ability, we face an NP-hard problem for which we devise an approximate solution. Both algorithms solve integer optimization problems by computing a sequence of binary optimizations, each one solved by graph cut techniques. Accordingly, we name the two algorithms PUMA, for phase unwrappping max-flow/min-cut. A set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state-of-the-art phase unwrapping algorithms.
相位展开是从模2π相位推断出绝对相位。本文介绍了一种用于相位展开的新的能量最小化框架。所考虑的目标函数是一阶马尔可夫随机场。只要相应的团块势是凸的，即对于相位展开经典Lp范数（p≥1），我们就提供一种精确的能量最小化算法。其复杂度为KT(n, 3n)，其中K是以2π单位测量的绝对相位域的长度，T(n, m)是具有n个节点和m条边的图中最大流计算的复杂度。对于由于其保持不连续性的能力而经常使用的非凸团块势，我们面临一个NP难问题，为此我们设计了一种近似解决方案。两种算法都通过计算一系列二进制优化来解决整数优化问题，每个二进制优化都通过图割技术来解决。因此，我们将这两种算法命名为PUMA，即相位展开最大流/最小割算法。一组实验结果说明了所提出方法的有效性及其与现有相位展开算法相比的竞争力。
