【作者】 付宇光；

【导师】 唐焕文；

【作者基本信息】 大连理工大学 ， 运筹学与控制论， 2002， 硕士

【摘要】 人脑的高级功能是自然界中最复杂的运动形式之一。在人脑高级功能的研究中，需要取得人脑各个脑区在受到刺激时的反映，采用PET、SPECT、fMRI等设备可以获得脑高级功能实验所需的具有较高分辨率的图像。鉴于成像过程中不可避免会有噪音干扰和由于被试运动引起的影像的失真和位置的偏移，有效的信号检测技术和图像处理技术在研究过程中是必不可少的。 脑功能成像技术是研究脑科学的重要工具，研究中通常需要将同一病人的多种模式成像结果或同一模式的时间序列结果结合起来分析，首先要解决的问题就是几幅图像的严格对齐问题，即所谓的图像配准。现行对医学图像配准的研究通常是采用修正的Gauss-Newton法，通过计算需配准图像和参考图像之间残差平方和的极小值，得到图像变换的最优解。本文在传统Gauss-Newton法的基础上，对其进行了改进，即在求搜索方向p时，引入了一种较为实用有效的求解线性方程组的算法。该算法的引入避免了Gauss-Newton法中矩阵求逆的过程，从而避免了Jacobi矩阵奇异时的舍入误差，提高了算法的计算速度和精度。 另外，针对Gauss-Newton法对迭代初值要求较高和容易陷入局部极小而达不到全局极值这些缺陷，本文对解决全局优化效果较好的模拟退火算法进行了相应的讨论。在本文中引入了一种改进的模拟退火算法模型——有记忆的模拟退火算法，该算法对迭代初值要求不高并通过记忆功能有效的避免了最终解不是整个搜索过程中的最优解的现象，从而提高了算法所得解的质量。 最后，本文通过实际算例对Gauss-Newton法和模拟退火两种算法进行了比较分析。更多还原

【Abstract】 The high function of human brain is one of the most complex activities in the world of nature. In the research of high brain function, we need gain the reflection of every brain area when they are stimulated. With the instruments such as PET, SPECT and fMRI etc, we can obtain the images with high resolution that we need in the experiment of high brain functional imaging. It is inevitable that there is some interference noise, positional shift and distortion of image caused by the movement of tested person, so effective signal detection and image processing technology is indispensable.Brain functional imaging is a kind of important tools in study of brain and life science. In research, we often need analysis the result of multimodal medical images of a single patient or time series images in combination, so it is necessary to register the brain functional images. Based on Gauss-Newton method, this paper proposes a practical algorithm when we search for the direction p in solving nonlinear least square problem. By using this algorithm, we needn’t resolve the inverse matrix in Gauss-Newton method, so we can get rid of the rounding error, by means of points-based register method, realize the higher precision registration of brain functional images.In addition, it is easy to reach a local extreme value when using Gauss-Newton method, so a proper initial iterative value is requested. On the other hand, Simulated Annealing Algorithm almost has no special need for the selection of initial iterative value, so the corresponding discussion about this algorithm is mentioned in the following of this paper.Last of all, comparison and analysis between Gauss-Newton method and simulated annealing algorithm are provided based on real computation instance.更多还原