马尔科夫随机场用于复杂流场的光学干涉层析重建的研究

发布时间：2018-03-21 08:02

本文选题：复杂流场　切入点：光学层析重建　出处：《深圳大学》2016年博士论文　论文类型：学位论文

【摘要】：复杂流场的测量主要应用于空气动力学以及爆轰等军事场合,具有重要意义。至少有两大特点使得测量困难,(1)内部环境苛刻,高温、高压、腐蚀等环境限制了接触式传感器的使用;(2)高速场,过程几近瞬态,在极短的时间内发生变化。而光学层析是计算机层析的一个分支领域,是非接触的不干扰待测物理场分布的测量技术,在复杂流场的众多应用领域展现了极大的优越性。其中干涉层析以干涉条纹为观测,具有灵敏度高、反应快等优点,在复杂流场测量具有较高的研究和实用价值。本文针对现有技术的缺陷,提出一个框架性的解决方案,即结合统计学、图论等现代工具,重点应用马尔科夫随机场理论对干涉层析中的几个关键问题进行建模并寻优,具有以下几点重要创新:(1)为光学层析重建领域提出一个全新的解决方案,即应用马尔科夫随机场理论,将光学层析重建问题涉及的多个关键技术统一于同一个理论框架之内;(2)提出一种基于反余弦及其区间反转相位恢复新方法,该方法实现简便,计算简单,在不同的相对载频下都拥有小而稳定的恢复误差及较好的恢复效果;(3)提出一种基于马尔科夫随机场的相位提取方法,此方法不依赖于空间载波,有效地从单幅干涉图中恢复相位差,应用场合更广泛;(4)提出一种基于马尔科夫随机场的图像重建方法,这一方法可在极少投影量下得到大大优于传统技术的结果,不仅可应用于二值层析问题,也可以应用于多像素值的情况。论文在上述的创新点上开展了大量研究工作,主要研究内容简述如下。(1)基于反余弦区间反转的相位恢复方法相位重建是干涉层析的首要解决的问题。论文分析了余弦函数正负号歧义问题,导出了反余弦相位和相位2π模之间的关系。由于在反余弦的(π,2π)区间需要对相位反转,将反转区间的确定问题转换为一个三段式折线拟合问题。利用遗传算法等优化方法求解了折线的最小均方拟合,且使用最小二乘法估计了干涉图的载频,进而获得最佳相位估计。仿真过程及结果表明,提出方法实现简便,计算简单,在各种相对载频下都拥有小而稳定的恢复误差及较好的恢复效果,相对于传统的傅里叶变换和条纹分析等方法,更适用于具有各种不同梯度大小的相位图。(2)基于马尔科夫随机场的相位提取方法符号不确定性是从单幅干涉图中恢复相位差的一个关键问题,本研究提出了一种基于马尔科夫随机场能量最小化的符号不确定性消除新方法。提出的方法使用马尔科夫随机场构建符号图中像素点之间的点对关系,这是“全局”与“局部”之间的折中。方法注意到相邻位置的符号反转时,干涉图反余弦的梯度方向图将有一个π大小的跳跃。利用这一信息建立了马尔科夫随机场的点对能量函数。为了进一步减少噪声影响,使用邻域直接平均和自适应滤波来取代光流,结果表明该法能正确地平滑梯度方向图用作随机场的输入。仿真结果表明方法有效地从单幅干涉图中恢复相位差,且不依赖于空间载波,应用场合更广泛。相位恢复的好坏直接影响层析重建的效果,因此前两部分研究内容为干涉层析重建提供了重要的技术支持。(3)基于马尔科夫随机场的切片图像重建方法从少量的投影数据中重建切片图像一直是一个具有挑战性的任务。本文将该问题数学表达为一个统计图模型推理问题。马尔科夫随机场可以简便整合各种先验信息,例如光滑先验,即离得近的像素之间具有较一致的灰度值。应用信任传播推理时遭遇高阶簇引起的指数级增长计算难题,本文提出了一个变量变换的技巧,可以将指数级计算量降为多项式计算量,即从Ο(MN-1)降至Ο((N-2)M2),从而获得一个快速和积推理算法。实践证实其有效性,即可在极少投影量下得到大大优于传统技术的结果,且不仅可应用于二值层析问题,也可以应用于多像素值的情况。(4)基于马尔科夫随机场的切片插值方法层析切片图像需要插值重建才能做到完整的体视化。本文针对传统数学插值的缺陷,提出了一种基于马尔科夫随机场的统计重建技术,对层析切片数据在垂线方向上建模,并使用全局优化算法模拟退火来实现寻优。这成为后续的层析物理场的智能理解的技术基础。上述关键技术统一于马尔科夫随机场理论框架,借助于统计学、模式识别等先进数学工具更高效更有效地寻找最优解,极大地丰富了复杂流场测量与光学层析重建技术。
[Abstract]:The measurement of complex flow field is mainly used in aerodynamics, detonation and other military applications, which is of great significance. There are at least two major characteristics of the measurement difficulties, (1) the internal environment of high temperature, high pressure, harsh, corrosive environment limits the use of non-contact sensor; (2) high speed field, almost instantaneous change in the process. Within a very short period of time. While the optical tomography is a subfield of computer tomography, is not interference measurement technology to measure the physical distribution of non contact, show great superiority in many application fields. The complex flow of interference fringes were observed by chromatography, with high sensitivity, fast response and other advantages that is high in complex flow field measurement research and practical value. This paper aims at the defects of the existing technology, puts forward a framework solution, which combines statistics, graph theory and other modern tools, focusing on the application of Markoff The random field theory of interference of several key problems in chromatography was applied to modeling and optimization, has the following innovation: (1) put forward a new solution for optical tomography reconstruction, namely the application of Markov random field theory, will involve the optical tomography reconstruction problem of multiple key technologies within the same unified the theoretical framework; (2) put forward a new method to restore the arccosine and interval based on phase inversion, this method is easy to realize, simple calculation, in the relative frequency under different have small and stable error and better recovery recovery effect; (3) proposed an extraction method based on Markov random phase. This method does not depend on the spatial carrier, effectively from the single interferogram in recovery phase difference applications more widely; (4) we propose an image reconstruction method based on Markov random field method, this method can be used in very little investment The results are much better than the traditional shadow volume, can be used not only in the value of two chromatography, can also be applied to multi pixel values. This paper carried out a lot of research work in the innovation, the main research contents are summarized as follows. (1) recovery method based on phase reconstruction phase anticosine interval inversion is to solve the problem of interferometric tomography. This paper analyzes the cosine function of sign ambiguity, the relationship between the arccosine phase and derived 2 pi mode. Because the arccosine of (PI 2, PI) interval needs to convert the problem to determine the phase inversion, inversion interval for a three segment line fitting the problem. By using the genetic algorithm optimization method to solve the linear least square fitting and least square method is used to estimate the carrier frequency of the interferogram, and then obtain the optimal phase estimation. The simulation process and results show that the proposed method. This simple, simple calculation, various relative carrier has a small and stable error recovery and recovery effect is better, compared with Fourier transform and fringe analysis of traditional methods, more suitable for the phase diagram with different gradient size. (2) Markoff random phase extraction method of uncertainty is from a single symbol interference is a key problem in the recovery phase difference based on this study, a method based on the Markoff energy minimization random symbol uncertainty elimination method. The proposed method uses pixels random field to construct symbolic figure Markoff point to the relationship, this is the "global" and "local" compromise between note that the sign reversal method. Adjacent position when the interference graph gradient direction cosine will jump a PI size. The establishment of Marco's with the use of this information The airport of the energy function. In order to further reduce the influence of noise, instead of using the neighborhood average optical flow directly and adaptive filtering, the results show that this method can correct horizontal slide direction diagram is used as the random input. The simulation results show that the method of interference effectively from a single figure in the recovery phase, and does not depend on the spatial carrier, application the occasion is more extensive. Phase recovery directly influences the tomographic reconstruction effect, so the research work of two parts for interferometric tomography reconstruction provides an important technical support. (3) based on Markov random slices like airport reconstruction method of the reconstructed slice image from the projection of a small amount of data has been a challenging task. The expression of the mathematical problem as a statistical inference problem. The graph model of Markov random field can easily integrate various prior information, such as that from a smooth prior. Between near pixels with gray values. The index is consistent with the application of trust propagation reasoning encountered high order cluster caused by the growth of computing problem, this paper proposes a variable transformation technique, exponential computation can be reduced to polynomial computation, namely from April (MN-1) to April ((N-2) M2) thus, to obtain a fast and integrated reasoning algorithm. Practice proves its effectiveness can be much better than the traditional technology results in little projection, and can be used not only in the value of two chromatography, can also be applied to multi pixel value. (4) with Markov chromatography slice interpolation method of airport section image interpolation reconstruction can achieve visualization based on the complete. Aiming at the defects of traditional interpolation, is proposed based on the Markov random field of statistical reconstruction technology, tomographic slice data modeling in the vertical direction, and the use of all Optimization algorithm simulated annealing to achieve the optimization. This technology as the basis for intelligent chromatography subsequent understanding of the physical field. The key technologies in unified Markov random field theory, using advanced mathematical tools in statistics, pattern recognition more efficiently and effectively find the optimal solution, greatly enriched the complex flow field and optical measurement the tomographic reconstruction technique.

【学位授予单位】：深圳大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O211.62

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