像素级图像融合及其相关技术研究
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摘要
经过三十多年的发展，多源传感器图像信息融合逐渐成为一门新兴的学科。多源传感器图像信息融合是指通过对两个或者多个传感器获得的关于同一场景的图像信息进行整合处理，以便获得一幅对该场景更精确、更可靠和更全面描述的图像。随着图像融合技术及其理论的进一步发展和完善，可以预见它将更广泛地应用到军事、医学、工业监测、地球遥感等领域。尽管图像融合的研究取得了很大的成就，但是由于图像融合面对很多新情况、新问题，使得图像融合的研究变得越来越重要。目前，国内关于图像融合的研究处于起步阶段，远远落后于国外，因此，有必要对图像融合进行深入的研究。本文对像素级图像融合在理论和技术方面进行了如下的研究：
(1)图像融合是一个病态的求逆问题，采用模拟退火算法求解能量最小化函数时速度很慢，且无法保证获得最优解，本论文采用图论为图像融合的能量最小化函数建立了相应的图模型，并采用图割理论进行优化求解，极大地提高了图像融合的求解速度，并能获得问题的全局最优解。
(2)在子空间和多尺度上对图像融合进行了研究。其一，采用二维主成分分析及控向金字塔分解方法，对多光谱和全色图像的融合进行了研究，同时还考虑了边缘的保护，实验表明该算法能够有效地改善图像的空间分辨率及减少光谱失真；其二，综合利用主成分分析、IHS变换及视觉驱动模型对医学PET图像和MRI图像融合进行了研究，该算法综合利用了三者的优点，能够有效地提高融合的空间分辨率，降低光谱失真；其三，基于特殊线性群理论提出了一种新的独立成分分析算法，应用该算法进行图像融合时可以有效地提高融合效果；最后，在最大似然估计理论和拉普拉斯金字塔分解算法上建立了一种新的图像融合算法，该算法有效的结合了估计理论和多尺度分解的优点，实验结果表明该算法能够获得比较好的融合效果。
(3)针对有噪源图像，为了更有效地提高空间分辨率和视觉效果，以及保护边界信息，提出了一种改进全变差融合算法，结合二阶优化模型，获得了一种新的融合算法。
(4)由于融合算法中存在很多求解矩阵特征值的问题，而神经网络在求解矩阵特征值时具有并行、快速和易于实现的优点，因此本论文系统研究了运用神经网络来求解矩阵特征值的算法，根据这些算法可以获得：实反对称矩阵全部特征值及其特征向量，特殊正交矩阵所有特征值及其特征向量，一般实矩阵虚部绝对值最大或最小特征值及其特征向量，一般实矩阵模最大或最小特征值及其特征向量，一般实矩阵实部最大和最小特征值及其特征向量，一般实矩阵实部绝对值最大特征值的实部。同时讨论了实反对称矩阵特征值求解的复神经网络算法，提出了求解一般实矩阵全部特征值的统一模型。
With the development of thirty years, the multisource sensors information fusionis gradually becoming a rising discipline. The multisource sensors image informationfusion need to integrate the images information of the same scene captured by two ormore sensors into a single image, which can describe the scene more accurately, reliablyand comprehensively. With the further development and improvement of image fusiontechnologies and its related theories, it can foresee that image fusion will be more widelyapplied to the fields of military, medical, industrial monitoring, remote sensing of theearth, and so on. Although great achievements have been made in the field of imagefusion, it still has many new situations and new issues to face for the image fusion, whichmakes image fusion become more important. At present, the domestic research on theimage fusion is just getting started, but is far behind the foreign counterpart. Therefore,it is necessary to carried out in-depth study on the image fusion. In this dissertation thefollowing works are focused on the researches of theories and technical issues of thepixel-level image fusion:
(1) The image fusion is an ill-posed inverse problem, and the use of the simulatedannealing algorithm for solving the energy minimization function is very slow, in thesame time, the obtain of the optimal solution for the problem can not be guaranteed,in this dissertation graph theory is applied to construct the corresponding graph modelfor energy minimization function of the image fusion, and the graph cuts theory is usedto optimize the solution, on one hand the speed of solving the image fusion problem isgreatly improved, on the other hand, the global optimal solution can also be obtained.
(2) Based on the subspace and the multi-scale method, extensive research on imagefusion have been carried out. First, the two-dimensional principal component analysis andsteerable pyramid decomposition is applied to fuse the multi-spectral and panchromaticimages, in addition, the algorithm about the edge protection is also taken into account.The simulation indicated that the proposed methods can effectively improve the spatialresolution and reduce the distortion of the spectral information; Second, the principalcomponent analysis, the IHS transform and visual driving model are comprehensivelyused to study the medicine images fusion of the PET and MRI images. The virtues of the three algorithm are combined and can improve the spatial resolution and reduce thedistortion of the spectral information. Third, a new independent component analysis al-gorithm(ICA) is proposed based on the special linear group theory. This algorithm canimprove the fusion effect greatly. At last, a new fusion method is proposed based onthe maximum likelihood estimation theory and the Laplacian pyramid decomposition al-gorithm, the algorithm effectively combines the virtues of spatial estimation theory andthe multi-scale decomposition, the experimental results show that the algorithm is able toobtain better fusion performance.
(3) For the noisy source image fusion, in order to improve the spatial resolutionand visual effect, and to protect the edge information, a modified total variation model isproposed, combined with the second-order optimization model, a new fusion algorithm isalso proposed.
(4) Because there are many matrices eigenvalue solution problems in the image fu-sion, and neural network is parallel, fast, and easy to be realized in the matrices eigenvaluesolution, this dissertation systematically studied the eigenvalue problems by neural net-works, and the followings can be obtained: all of the eigenvalues and the correspondingeigenvectors of real antisymmetric matrices, all of the eigenvalues and the correspondingeigenvectors of special orthogonal matrices, eigenvalues and the corresponding eigen-vectors of imaginary part absolute largest or smallest in the eigenvalues of general realmatrices, eigenvalues and the corresponding eigenvectors of modulus largest or smallestin the eigenvalues of general real matrices, eigenvalues and the corresponding eigenvec-tors of real part largest or smallest in the eigenvalues of general real matrices, and the realpart of eigenvalues with real part absolute largest in the eigenvalues of general real matri-ces. In the same time, a complex neural networks algorithm is also discussed to solve theeigenvalues of real antisymmetric matrices, and a unified model is proposed to obtain alleigenvalues of general real matrices.
(1)图像融合是一个病态的求逆问题，采用模拟退火算法求解能量最小化函数时速度很慢，且无法保证获得最优解，本论文采用图论为图像融合的能量最小化函数建立了相应的图模型，并采用图割理论进行优化求解，极大地提高了图像融合的求解速度，并能获得问题的全局最优解。
(2)在子空间和多尺度上对图像融合进行了研究。其一，采用二维主成分分析及控向金字塔分解方法，对多光谱和全色图像的融合进行了研究，同时还考虑了边缘的保护，实验表明该算法能够有效地改善图像的空间分辨率及减少光谱失真；其二，综合利用主成分分析、IHS变换及视觉驱动模型对医学PET图像和MRI图像融合进行了研究，该算法综合利用了三者的优点，能够有效地提高融合的空间分辨率，降低光谱失真；其三，基于特殊线性群理论提出了一种新的独立成分分析算法，应用该算法进行图像融合时可以有效地提高融合效果；最后，在最大似然估计理论和拉普拉斯金字塔分解算法上建立了一种新的图像融合算法，该算法有效的结合了估计理论和多尺度分解的优点，实验结果表明该算法能够获得比较好的融合效果。
(3)针对有噪源图像，为了更有效地提高空间分辨率和视觉效果，以及保护边界信息，提出了一种改进全变差融合算法，结合二阶优化模型，获得了一种新的融合算法。
(4)由于融合算法中存在很多求解矩阵特征值的问题，而神经网络在求解矩阵特征值时具有并行、快速和易于实现的优点，因此本论文系统研究了运用神经网络来求解矩阵特征值的算法，根据这些算法可以获得：实反对称矩阵全部特征值及其特征向量，特殊正交矩阵所有特征值及其特征向量，一般实矩阵虚部绝对值最大或最小特征值及其特征向量，一般实矩阵模最大或最小特征值及其特征向量，一般实矩阵实部最大和最小特征值及其特征向量，一般实矩阵实部绝对值最大特征值的实部。同时讨论了实反对称矩阵特征值求解的复神经网络算法，提出了求解一般实矩阵全部特征值的统一模型。
With the development of thirty years, the multisource sensors information fusionis gradually becoming a rising discipline. The multisource sensors image informationfusion need to integrate the images information of the same scene captured by two ormore sensors into a single image, which can describe the scene more accurately, reliablyand comprehensively. With the further development and improvement of image fusiontechnologies and its related theories, it can foresee that image fusion will be more widelyapplied to the fields of military, medical, industrial monitoring, remote sensing of theearth, and so on. Although great achievements have been made in the field of imagefusion, it still has many new situations and new issues to face for the image fusion, whichmakes image fusion become more important. At present, the domestic research on theimage fusion is just getting started, but is far behind the foreign counterpart. Therefore,it is necessary to carried out in-depth study on the image fusion. In this dissertation thefollowing works are focused on the researches of theories and technical issues of thepixel-level image fusion:
(1) The image fusion is an ill-posed inverse problem, and the use of the simulatedannealing algorithm for solving the energy minimization function is very slow, in thesame time, the obtain of the optimal solution for the problem can not be guaranteed,in this dissertation graph theory is applied to construct the corresponding graph modelfor energy minimization function of the image fusion, and the graph cuts theory is usedto optimize the solution, on one hand the speed of solving the image fusion problem isgreatly improved, on the other hand, the global optimal solution can also be obtained.
(2) Based on the subspace and the multi-scale method, extensive research on imagefusion have been carried out. First, the two-dimensional principal component analysis andsteerable pyramid decomposition is applied to fuse the multi-spectral and panchromaticimages, in addition, the algorithm about the edge protection is also taken into account.The simulation indicated that the proposed methods can effectively improve the spatialresolution and reduce the distortion of the spectral information; Second, the principalcomponent analysis, the IHS transform and visual driving model are comprehensivelyused to study the medicine images fusion of the PET and MRI images. The virtues of the three algorithm are combined and can improve the spatial resolution and reduce thedistortion of the spectral information. Third, a new independent component analysis al-gorithm(ICA) is proposed based on the special linear group theory. This algorithm canimprove the fusion effect greatly. At last, a new fusion method is proposed based onthe maximum likelihood estimation theory and the Laplacian pyramid decomposition al-gorithm, the algorithm effectively combines the virtues of spatial estimation theory andthe multi-scale decomposition, the experimental results show that the algorithm is able toobtain better fusion performance.
(3) For the noisy source image fusion, in order to improve the spatial resolutionand visual effect, and to protect the edge information, a modified total variation model isproposed, combined with the second-order optimization model, a new fusion algorithm isalso proposed.
(4) Because there are many matrices eigenvalue solution problems in the image fu-sion, and neural network is parallel, fast, and easy to be realized in the matrices eigenvaluesolution, this dissertation systematically studied the eigenvalue problems by neural net-works, and the followings can be obtained: all of the eigenvalues and the correspondingeigenvectors of real antisymmetric matrices, all of the eigenvalues and the correspondingeigenvectors of special orthogonal matrices, eigenvalues and the corresponding eigen-vectors of imaginary part absolute largest or smallest in the eigenvalues of general realmatrices, eigenvalues and the corresponding eigenvectors of modulus largest or smallestin the eigenvalues of general real matrices, eigenvalues and the corresponding eigenvec-tors of real part largest or smallest in the eigenvalues of general real matrices, and the realpart of eigenvalues with real part absolute largest in the eigenvalues of general real matri-ces. In the same time, a complex neural networks algorithm is also discussed to solve theeigenvalues of real antisymmetric matrices, and a unified model is proposed to obtain alleigenvalues of general real matrices.
引文
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