概率统计方法在微波生物医学成像和雷电电磁效应评估中的应用

发布时间：2018-05-08 19:32

本文选题：微波生物医学成像 + 逆散射　；参考：《四川大学》2005年博士论文

【摘要】：本文包含微波生物医学成像和雷电电磁效应评估两方面的研究内容。微波成像作为一种典型的电磁逆散射问题,具有重要的理论研究价值,不仅如此,它在生物医学成像领域具有的潜在优势也使其具有很高的应用价值。另一方面,由于电子系统向小型化、微型化发展的趋势使它们对瞬态电磁现象的敏感程度增加,雷电活动作为重要的瞬态电磁现象之一,其电磁效应评估研究得到日益重视。本文的主要工作包括: 1、对微波成像(逆散射问题)的一般数学理论和算法进行了研究。指出:①逆散射问题病态性的根本解决办法是增加有效信息,包括测量信息和先验信息(额外信息);②研究测量信息的“质”有助于选取更加合理有效的测量方式;③无论研究者是否存在向逆过程加入额外信息的主观意图,现有的两大类逆散射算法——结合正则化技术的确定性方法和全局随机搜索方法,都“不由自主地”包含了增加额外信息的处理;④当优化技术所求出的某种意义下的最优解与真实解之间的误差难以确定时,考虑整个解集(即进行整体推断)就显得相当重要。 2、对同轴线中分层媒质电特性重建问题(可视为一维逆散射问题)中测量信息的“质”进行了初步研究。首先从传输线理论导出的模型出发,采用数学分析与数值实验相结合的办法对问题的病态性进行研究,在此基础之上,进一步探讨如何获得更多有效的信息以改善问题的病态特性,对不同测量条件(在不同频率下或在不同负载阻抗下测量)所得测量信息在保证重建结果的唯一性和减
[Abstract]:This paper includes two aspects of microwave biomedical imaging and lightning electromagnetic effect evaluation. As a typical electromagnetic inverse scattering problem, microwave imaging has important theoretical research value, not only that it has potential advantages in biomedical imaging field, but also has a high application value. On the other hand, due to the trend of miniaturization and miniaturization of electronic systems, their sensitivity to transient electromagnetic phenomena is increased. As one of the important transient electromagnetic phenomena, the research on the evaluation of electromagnetic effect of lightning is paid more and more attention. The main work of this paper includes: 1. The general mathematical theory and algorithm of microwave imaging (inverse scattering problem) are studied. It is pointed out that the fundamental solution to the ill-condition of the problem is to increase the effective information, including the measurement information and the prior information. (2) to study the "quality" of the measurement information is helpful to select more reasonable and effective measurement methods. (3) whether or not the researcher has the subjective intention to add additional information to the inverse process, there are two main classes of inverse scattering algorithms: deterministic method combined with regularization technique and global random search method. "involuntarily" includes the processing of adding additional information when the error between the optimal solution and the real solution in a sense derived by the optimization technique is difficult to determine, It is important to consider the entire set of solutions (that is, to infer the whole). 2. The "quality" of measurement information in the problem of electrical property reconstruction of layered media in coaxial line (which can be regarded as one-dimensional inverse scattering problem) is studied preliminarily. Based on the model derived from the transmission line theory, the morbid property of the problem is studied by combining mathematical analysis with numerical experiments. How to obtain more effective information to improve the pathological characteristics of the problem is further discussed. The uniqueness and subtraction of the reconstruction results can be ensured by the measurement information obtained under different measurement conditions (measured at different frequencies or under different load impedances).
【学位授予单位】：四川大学
【学位级别】：博士
【学位授予年份】：2005
【分类号】：R311

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