Phase unwrapping of MR phase images using Poisson equation

The authors have developed a technique based on a solution of the Poisson equation to unwrap the phase in magnetic resonance (MR) phase images. The method is based on the assumption that the magnitude of the inter-pixel phase change is less than pi per pixel. Therefore, the authors obtain an estimate of the phase gradient by "wrapping" the gradient of the original phase image. The problem is then to obtain the absolute phase given the estimate of the phase gradient. The least-squares (LS) solution to this problem is shown to be a solution of the Poisson equation allowing the use of fast Poisson solvers. The absolute phase is then obtained by mapping the LS phase to the nearest multiple of 2 K from the measured phase. The proposed technique is evaluated using MR phase images and is proven to be robust in the presence of noise. An application of the proposed method to the 3-point Dixon technique for water and fat separation is demonstrated.     

Phase unwrapping via graph cuts.

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.     

双频外差结合相位编码的相位解包裹方法

为了使用高频条纹进行一次外差完成相位解包裹,实现高精度测量,提出了双频外差结合相位编码的相位解包裹方法。首先,用两组正弦条纹获得两个包裹相位,进行外差处理得到外差相位;其次,相位编码条纹得到条纹级次后对外差相位展开;最后,由连续的外差相位对两个包裹相位进行展开,用最高频率的连续相位求得物体的相位信息。实验结果表明:RMS误差为0.038 mm。双频外差合成的周期不需要覆盖整个视场,打破了传统双频外差方法对频率选择的限制,可以用更高频率的条纹进行高精度测量。克服了相位主值误差对使用更高频率条纹进行高精度测量的局限性。     

时间位相展开方法研究进展

时间位相展开是位相测量领域内的一种很重要的位相展开方法,被广泛应用于干涉型和结构照明型计量领域中,包括散斑干涉与剪切干涉计量、波长扫描干涉术、先弹测量、位相测量轮廓术、傅立叶变换轮廓术等领域。本文详细分析了近十年所提出的时间位相展开算法的基本原理,讨论和比较了各种算法的设计方法、计算公式和适用范围,对时间位相展开方法的最新进展和应用前景进行了较全面的分析和评述。     

Hierarchical network flow phase unwrapping

The well-studied interferometric synthetic aperture radar (InSAR) problem for digital elevation map generation involves the derivation of topography from the radar phase. The topography is a function of the full phase, whereas the measured phase is known modulo 2/spl pi/, necessitating the process of recovering full phase values via phase unwrapping. This mathematical process becomes difficult through the presence of noise and phase discontinuities. This paper is motivated by research which models phase unwrapping as a network-flow minimization problem. A major limitation is that often a substantial computational effort is required to find solutions. Commonly, these phase images are huge (/spl Gt/10 million pixels), and obviously the sheer size of the problem itself makes phase unwrapping challenging. This paper addresses the development of a computationally efficient hierarchical algorithm, based on a "divide-and-conquer" approach. We have shown that the phase-unwrapping problem can first be partitioned into independent phase-unwrapping subproblems, which can further be recombined to produce the unwrapped phase. Interestingly, the recombination step itself can be interpreted as an unwrapping problem, for which a modified network-flow solution applies! In short, this paper develops a parallelization of the network-flow algorithm, allowing images of virtually unlimited size to be unwrapped and leading to dramatic decreases in the algorithm execution time.     

可靠度导引的相位解包裹算法

设计实现了基于可靠度导引的相位解包裹算法。该算法首先在像素可靠度的基础上计算邻接线可靠度,然后根据邻接线可靠度的高低规划解包裹路径。仿真和实测结果表明,该算法可以有效避免误差扩散引起的拉线现象,提高解包裹相位的可靠性。     

相位解包裹中欠采样问题的实验研究

为了解决相位解包裹时由于相位变化快而出现的欠采样问题,采用剪切干涉的原理建立光场,利用加权离散余弦变换算法求解泊松方程的方法,实现了对横向剪切最小二乘相位解包裹算法的改进。在理论分析的基础上给出了具体的相位解包裹算法,并通过实验研究验证了改进后算法的可行性。结果表明,改进后的算法能够有效地避免由相位变化过快带来的欠采样问题。     

相位展开的6种算法比较

相位展开算法主要可以分为路径跟踪算法和全局展开算法。为了比较这些算法的性能,采用计算机模拟斜面和高斯面,并加入不同程度噪声产生包裹相位;从两大类中各选取3种比较典型的算法分别对其进行相位展开,计算它们的均方根误差;最后对实验数据进行比较和理论分析。结果表明,基于网络规划的最小费用流算法和基于贝叶斯推断的ZπM算法是较为有效的算法,在实际应用中值得选择和改进。     

A model-based method for phase unwrapping

Presents a model-based phase unwrapping method which represents the unwrapped phase function by a truncated Taylor series and a residual function. An efficient, noniterative computational algorithm is also proposed for calculating the model parameters from the phase derivatives. Sample experimental results are shown to demonstrate the effectiveness of the algorithm for extracting unwrapped phase images from two-dimensional (2-D) magnetic resonance imaging (MRI) data.     

Modifled nearest neighbor phase unwrapping algorilthm

The presences of noise and regions undersampling ininterference phasei mages will introduce phaseinconsist-encies or residues,which make the phase unwrappingvery complex.To solve this problem,a wide variety ofphase unwrapping algorithms have been suggeste…     

Two-dimensional phase unwrapping using wavelet transform

A method for solving the least squares two-dimensional phase unwrapping problem is presented. This technique is based on the multiresolution representation of a linear system using the discrete wavelet transform. By applying the wavelet transform to the original system, a better convergence condition of an equivalent new system can be achieved     

一种改进的菱形相位展开算法

菱形相位展开算法以菱形为路径进行相位展开, 具有展开速度快、易理解等特点而倍受亲睐,但是 当展开路径上遇到不可靠点时相位展开容易出错,并向后累计,形成拉线或孤岛现象。因此 ,本文提出一 种改进的菱形相位展开算法,先用大津法对调制度进行二值化形成基本模版,并以该模版非 零区域为导航 找出截断相位分布中的极点,通过对极点的所在位置进行标记进而生成极点模板;再根据基 本模版与极点 模板将极点与不可靠点进行隔离,从而对可靠点进行相位展开;最后根据相位的连续性原则 ,利用相位逼 近和插值拟合方法校正不可靠点处的相位,从而得到完整并且逼真的相位展开结果。实验结 果验证所提算 法的可行性和有效性,表明改进菱形相位展开算法可以有效地避免相位展开中的拉线和孤岛 现象。     

On frequency-domain and time-domain phase unwrapping

Time-domain phase unwrapping of analytic or complex functions of time is an unavoidable operation when processing such signals within an FM-modeling framework or when attempting to establish the instantaneous frequency of such signals. With the help of an alternate derivation of his equations, Tribolet's frequency-domain phase unwrapping algorithm is easily rewritten for time-domain application. The time derivative of the argument of the signal, a quantity needed in these modified equations, is developed and furthermore recognized to be proportional to the instantaneous frequency of the signal.     

Least-squares two-dimensional phase unwrapping using FFT's

A solution of the least-squares two-dimensional phase-unwrapping problem is presented that is simpler to understand and implement than previously published solutions. It extends the phase function to a periodic function using a mirror reflection, and the resulting equation is solved using the Fourier transform     

基于标记理论和相位滤波的相位解缠绕算法

相位解缠绕是磁共振成像技术应用中准确获取相位信息的关键所在,如温度监控,油水分离,测定血流速度等.然而,由于磁共振成像噪声比较严重,而且组织交界区域附近相位本身就存在突变,造成解缠绕的精度下降.本文将相位解缠绕转化为计算机视觉中的标记问题,并构造出相应的能量函数,为利用网络优化对其求解提供方便.同时,针对磁共振相位解缠绕中的噪声问题,本文提出一个新的滤波方法,可以高效地消除噪声导致的解缠绕的不一致性.通过仿真实验和磁共振图像的相位解缠绕实验,表明本文方法相位解缠绕精度更高,且计算速度快.     

合成孔径雷达干涉测量中的相位展开

合成孔径雷达干涉测量技术 (InSAR)是以合成孔径雷达复数据提取的相位信息作为信息源来获取地表的三维信息和变化信息的一项技术。相位展开是InSAR数据处理中的关键步骤之一。本文介绍了合成孔径雷达干涉测量的原理 ,重点讨论了InSAR中的相位展开算法 ,特别对与路径有关的算法和与路径无关的算法进行了分析 ,比较了各类方法的优缺点。指出一些在结构照明型计量中有效的相位展开算法也可以用于合成孔径雷达干涉测量之中的相位展开     

区域标记法位相展开

在干涉型和结构照明型计量领域中 ,对具有病态特性的截断位相进行有效位相展开是这一领域中关键步骤之一。本文基于位相展开过程中出现的一些问题提出了一种新的算法 ,该算法利用区域标记的方法并结合虚拟极点的概念 ,针对展开过程中经常出现的由于极点问题处理不当造成的错误展开情况进行合理展开 ,以期获得更加合理的结果。本文给出的实验结果证实了这一算法的有效性     

Interferometric SAR phase unwrapping using Green's formulation

Any method that permits retrieving full range (unwrapped) phase values starting from their (-π,π) determination (wrapped phase) can be defined as a phase unwrapping technique. This paper addresses a new procedure for phase unwrapping especially designed for interferometric synthetic aperture radar applications. The proposed algorithm is based on use of Green's first identity. Results on simulated as well as on real data are presented. They both confirm the excellent performance of the procedure     

改进的阶梯相位去包裹算法研究

为减少投影条纹数量,提高测量速度,提出了一种 改进的阶梯相位去包裹算法。算法 采用彩色条纹投影测量物体三维形貌,将正弦和阶梯相位条纹分别输入彩色图像的红 色和蓝色通道构成彩色条纹,由DLP投影仪将四步相移彩色条纹投影到待测物体上,由彩色 CCD相机采集。利用颜色分离技术得到2组四步相移条纹图,其中一组为4幅正弦条纹,由四 步相移法求得正弦条纹包裹相位,另一组4幅阶梯相位编码条纹图,由与正弦条纹周期一致 的阶梯相位构成,经阶梯相位解码确定条纹级次,利用自校正算法去除条纹级次噪点后,实 现相位去包裹。进行了实际测量,结果表明,本方法 测量精度与采用四步相移法相当,但只需4幅条纹图,有效减少了投影和采集的条纹数量, 提高了测量速度。     

Least squares phase unwrapping in wavelet domain

Two-dimensional phase unwrapping is an important processing step in some coherent imaging applications. Least squares phase unwrapping is one of the robust techniques used to solve two-dimensional phase unwrapping problems. However, owing to its sparse structure, the convergence rate is very slow, and some practical methods have been applied to improve this condition. A new method for solving the least squares two-dimensional phase unwrapping problem is presented. This technique is based on the multiresolution representation of a linear system using the discrete wavelet transform. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels. Fast convergence in separate coarse resolution levels makes the overall system convergence very fast.