Research On Markov Random Fields With Application To Interferometric Tomographic Reconstruction

Measuring complex flow field is mainly used in the field of aerodynamics and other military detonation, which is of great significance. There are at least two characteristics making the measurement difficult:(1) internal environment is harsh, such as high temperature, high pressure, corrosion environment limits the touch sensor;(2) the flow is in high-speed, almost transient process, in a very short period of time change. Optical tomography is an important branch of computer tomography. It is a non-contact measurement technique that does not interfere with the distribution of physical fields. It shows great superiority in many fields of complex flow field. The interference tomography has the advantages of high sensitivity and fast response, etc., which has high research and practical value in the measurement of complex flow field.Considering the defects of the existing technology, in this thesis, we put forward a framework of solution, which combines statistics, graph theory and other modern tools. We focus on the application of Markov random fields theory to the optical interference tomography in several key problems. In this thesis there are important innovations as follows.(1) In the field of optical tomography reconstruction we proposed a novel solution, that is, applying Markov random field theory, the optical tomographic reconstruction key techniques can be unified within one same theoretical framework.(2) A new method based on the inverse cosine was proposed to retrieve phase difference. The method is simple and easy to implement. It has a small and stable retrieval error and better performance in all kinds of phase situations.(3) We proposed a Markov random fields based phase extraction method. This method does not rely on any spatial carrier and can retrieve phase effectively from a single interferogram. This leads to more applications.(4) A novel image reconstruction method based on Markov random fields was developed in this thesis. The method can work with a very small amount of projections and greatly outperforms the conventional techniques. It can be used not only in binary tomography problem, but also in the multi pixel value case.In this thesis, the research results and the main contents of this thesis are as follows.(1) An inverse cosine method for phase retrievalPhase retrieval is one of the most important techniques for the optical interference tomography. In this thesis, the problem of ambiguity of the cosine function is analyzed, and the relationship between the inverse cosine phase and the phase 2? mode is derived. Because of the need of phase inversion for certain range of the inverse cosine, the determination of the inversion range is converted to a three fold line fitting problem. We use a genetic algorithm and other optimization methods to solve the minimum mean square fitting problem, and employ a least square method to estimate the carrier frequency of the interferogram. The best phase estimation is then achieved. The simulation procedure and the results show that compared with the traditional Fourier transform and fringe analysis and other methods, the proposed method is simple and convenient to implement, in all cases has small and stable error and better recovery performance. It is also more suitable for those interferograms with a variety of different gradient magnitude.(2) Phase recovery based on Markov random fieldsThe uncertainty of sign is a key factor of the phase recovery from a single interferogram. This thesis proposed a method based on energy minimization to eliminate the sign uncertainty. The method used a Markov random field to model the sign relationship between pixels in the modulated phase map. This is a compromise between "global" and "local". We notice that when there is a sign reversal between adjacent pixel positions, there will be a ? jump in the gradient orientation map of the interferogram's inverse cosine. The pairwise clique potential of the Markov random field is then constructed using this information. In order to further reduce the noise influence, we replace the often-used optical flow with the neighborhood averaging and adaptive filtering. The results show that the method can correctly smooth the gradient figure as an input of the random field. Simulation results show that our method can effectively retrieve the phase difference from a single interference graph and does not depend on any spatial carrier. This leads to more extensive applications. Phase field reconstruction has a direct impact on the effect of tomographic reconstruction. Therefore the research of the first two parts provides an important technical support for the reconstruction of the interferometric tomography.(3) Markov random fields based tomographic image reconstruction methodTomographic image reconstruction from a small number of projection data is always a challenging task. In this thesis, the problem is formulated as a statistical graph model reasoning problem. Markov random fields can be easily integrated with various prior information, such as smoothness, that is, neighbor pixels have a larger probability to take a closer value. When applying belief propagation inference, however, we encounter high-level cliques leading to the exponential growth of computing problem. In this thesis we present a variable changing technique. The exponential computational complexity can be reduced to a polynomial computational complexity, from-?1()NM to ?((-))2N1 M, such that we obtain a fast sum-product inference algorithm. In practice, numerical results demonstrate that it is effective and can get much better results than the traditional technologies, and can be applied to the case of multi-pixel-values.(4) Slice interpolation based on Markov random fieldsTomographic slice images need to be reconstructed in order to achieve complete volume visualization. In this thesis, considering the defects in traditional mathematical interpolation, a statistical reconstruction techniques based on Markov random fields is proposed. The method models the pixel values along the line perpendicular to the slices. Using simulated annealing algorithm as global optimizer for the Markov random field yields promising result. This becomes a technical basis for the intelligent understanding of the tomography of the physical field.The key technologies stated above are united in the theory framework of Markov random fields. We can achieve effective and efficient results with the help of statistics, pattern recognition and other advanced mathematical tools. This greatly enriches the measurement of complex flow field and the optical tomography reconstruction technique.