基于子空间优化方法的非线性电磁场逆成像算法研究

发布时间：2018-02-15 08:14

本文关键词： 线性算法非线性算法一阶Born近似格林函数二阶Born近似子空间优化　出处：《南昌大学》2015年硕士论文　论文类型：学位论文

【摘要】：随着时代的发展,微波成像技术的运用领域也越来越多,其在日常生活和军事领域的应用所占的比例越来越重,传统的微波成像算法已经不能满足人们日常需求。因此,开展与微波成像相关的研究不管是对信息时代的国防还是逐步高度发展的社会都具有重要意义。对微波成像研究是世界前沿性课题,其主要功能是对目标成像,因此如何提高微波成像效果和求解目标的电性参数是研究微波成像技术的主要研究内容之一。本文主要研究了二阶Born近似和非线性算法子空间优化方法,并通过实验分析对比二阶Born近似和子空间优化方法的优劣性。针对二阶Born近似,本文基于一阶Born近似推导出二阶Born近似,并将其线性化,然后利用不精确牛顿算法对目标成像。考虑如何优化迭代算法,减少计算代价,并在多发多收的情况下,考虑如何将多个发射天线时的成像效果进行揉合。针对子空间优化方法,本文利用修正后的目标函数对目标进行成像,格林函数采用零阶二类汉克尔函数,并通过相关理论推导出子空间优化相关参数的表达式,通过选取适当截断点,计算出确定部分感应电流,再通过迭代优化得出模糊部分感应电流,最后确定目标网格内的总电场,反演出目标的相对介电常数,从而对目标成像。本文实验数据来源于法国马赛市菲涅尔研究所。实验表明,在利用二阶Born近似对单目标成像时,其结果较好的反映出目标的位置和大小,而对于目标的介电常数,在反演结果中并不能较好的表现出来,另外,对多目标成像时,其结果较差。而当利用非线性电磁逆成像算法子空间优化对目标成像时,不仅可以较为准确的反应目标的位置大小,同时也能较好的计算出目标的介电常数。另外,子空间优化方法在对多目标成像时,也能较好的反映出目标的各种几何参数和介电常数,但计算代价较大。因此,非线性算法子空间优化方法在对目标成像时表现出更高的准确性。
[Abstract]:With the development of the times, the application of microwave imaging technology is more and more, its application in daily life and military field is more and more heavy, the traditional microwave imaging algorithm can no longer meet the daily needs of people. The research related to microwave imaging is of great significance not only to national defense in the information age, but also to a society with a high degree of development. Microwave imaging is a leading subject in the world, and its main function is the imaging of targets. Therefore, how to improve the effect of microwave imaging and solve the electrical parameters of the target is one of the main research contents of microwave imaging technology. In this paper, we mainly study the second-order Born approximation and nonlinear algorithm subspace optimization method. The advantages and disadvantages of the second-order Born approximation and the subspace optimization method are compared by experiments. For the second-order Born approximation, the second-order Born approximation is derived based on the first-order Born approximation and linearized. Then we use the inexact Newton algorithm to image the target. Consider how to optimize the iterative algorithm, reduce the computational cost, and in the case of multiple collection, Considering how to combine the imaging effects of multiple transmit antennas, the modified objective function is used to image the target, and the Green function uses the zero-order Hankel function for subspace optimization. The expression of subspace optimization parameters is deduced by correlation theory. By selecting the appropriate truncation point, the partial inductive current is calculated and the fuzzy partial inductive current is obtained by iterative optimization. Finally, the total electric field in the target grid and the relative dielectric constant of the target are determined. The experimental data are obtained from the Fresnel Institute in Marseille, France. The experimental results show that the second order Born approximation is used to image a single target. The results reflect the position and size of the target well, but the dielectric constant of the target is not well represented in the inversion results. The results are not good. When the nonlinear electromagnetic inverse imaging algorithm is used to optimize the imaging of the target in subspace, not only the position of the target can be accurately reflected, but also the dielectric constant of the target can be calculated. The subspace optimization method can also reflect all kinds of geometric parameters and dielectric constant of the target, but the calculation cost is high. The subspace optimization method of nonlinear algorithm is more accurate in imaging target.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN015;TP391.41

【共引文献】