用于非均匀介质重建的迭代算法收敛性的研究

研究轴对称二维非均匀介质重建迭代算法的收敛性问题。首先借助于玻恩近似将非线性积分方程线性化；然后，利用玻恩迭代法和变形玻恩迭代法，由散射场数据对轴对称二维非均匀介质进行重建。通过几个例子研究了影响迭代算法收敛性的几种因素，如迭代算法本身、积分离散化后的网格划分、正则化方法中的正则化参数选取等。     

低频电磁场重建二维非均匀介质的有效方法

将玻恩迭代和变形玻恩迭代两种方法用于低频二维非均匀介质电导率的重建。利用上述两种方法求解非线性积分方程。用正则化方法对解加上约束克服重建问题中解的非唯一性和不稳定性。数值计算表明，两种迭代方法都可用于二维非均匀介质电导率的重建。同玻恩迭代法相比，变形玻恩迭代法显示出更快的收敛性，而同变形玻恩迭供法相比，玻恩迭代法的抗噪声能力更强。     

改善非均匀介质重建中解稳定性的方法

本文提出了改善轴对称二维非均匀介质重建中解稳定性的方法，第一，通过迭代算法本身改善解的稳定性；第二，提出一种混合玻恩迭代方法，它既提高解的收敛性也改善解的稳定性；第三，通过改变正则化方法中正则化参数来改善解的稳定性。我们也研究了最小二乘法中解的稳定性和收敛性。给出几个数值例子用来显示这些方法的优越性。     

轴对称二维非均匀介质的快速反演方法

首先采用变分原理和非线性积分方程推导出反演方程，然后利用玻恩迭代法对轴对称二维非均匀介质分布进行了反演。通过计算实例表明，该方法的收敛速度比玻恩迭代法快得多，在迭代前期与变形玻恩迭代法相当，而在迭代后期比变形玻恩迭代法的收敛速度更快；同时，每次迭代所需时间虽然多于玻恩迭代法，但明显少于变形玻恩迭代法。该方法同时具备了玻恩和变形玻恩迭代法两者的优点。     

用变形玻恩迭代法反演电导率的二维非均匀分布

本文把变形玻恩迭代方法用于求解二维轴对称逆散射问题。该方法提供一种迭代收敛较快的反演成像算法。利用对称轴上２０ｋＨｚ电场的测量值在二维非均匀介质中对电导率分布进行反演。首先给出对于未知电导率分布的非线性积分方法，并用玻恩近似使积分方程线性化，然后用吉洪诺夫与正则化方法求出电导率分布。在迭代过程中，数值模式匹配法用于求解正演场．数值实例表明，用简单的对称轴上测量场能得到好的好的成像结果。     

电磁场与微波技术

0441,,U3U了Z勺改善非均匀介质里建中解稳定性的方法/张业荣,聂在平,漆兰芬(电子科技大学)“电子学报一1998,26(9).一1一6文中提出了改善轴对称二维非均匀介质重建中解稳定性的方法.第一,通过迭代算法本身改善解的稳定性;第二,提出一种混合玻恩迭代方法,它既提高解的收敛性也改善解的稳定性;第三,通过改变正则化方法中正则化参数来改善解的稳定性‘也研究了最小二乘法中解的稳定性和收敛比.给出几个数值例子用于显示这些方法的优越性.图5参5(金)各向同性手征媒质均匀填充手征波导中的拐合波方程/张玉俊(华东电子工程研究所)“电子学报.一1…     

轴对称二维位场的变形玻恩迭代的反演

本文将变形玻恩迭代方法用于处理轴对称二维非均匀介质分布的电导率反演问题。众所周知，横磁场的反演比横电场的反演的非线性程序更高。本文选用了收敛速度快而效果好的变形波恩迭代反演方法。而离散非线性积分方程所得矩阵方程的病态特性用吉洁诺夫正则化方法来克服，再用共因梯度方法求解，在每次迭代过程中采用了快速的半解析阗数值的高效正演方法，本文用它半解析地表达出反演中所需计算的格林函数的偏导数；并在此基础上半解析     

轴对称二维位场的变形玻恩迭代反演

本文将变形玻恩迭代方法用于处理轴对称二维非均匀介质分布的电导率反演问题众所周知，横磁场的反演比横电场的反演的非线性程度更高．本文选用了收敛速度快而效果好的变形波恩迭代反演方法．而离散非线性积分方程所得矩阵方程的病态特性用古洪诺夫正则化方法来克服，再用共轭梯度方法求解在每次选代过程中采用了快速的半解析半数值的高效正演方法，本文用它半解析地表达出反演中所需计算的格林函数的偏导数；并在此基础上半解析地求出了反演的非线性积分方程中的积分运算，从而大大提高了反演速度和精度     

变形玻恩迭代法用于非均匀分布地层电导率的重建

借助于玻恩近似将ＴＥ波的非线性积分方程线性比，由井轴上测量到的低频近测量数据，利用变形玻恩迭代方法对二维非均匀地层电导率进行重建和反演。用吉洪诺夫正叫化方法处理重建中 病态矩阵方程。     

用迭代方法和双共轭梯度法重建二维电导率剖面分布

本文着重阐述采用积分方程的迭代方法并结合双共轭梯度（ＢＣＧ）法对低频近声非均匀背景介质中二维轴对称电导率剖面的反演,并仅用ｚ向采集的数据进行目标重建。首先,基于等反演目标区内、外的电场积分方程。建立超反演积分方程,将积分方程离散化为矩阵方程用迭代方法求解目标区电导率分布。在每次迭代过程中,格林函数不断被更新。同时用正则人垭消除解的不适定性。文中利用不完备的测量数据对复杂的电导率同进行了反演。模拟结     

用修正玻昂迭代法重建复杂介质结构

着重阐述了将修正玻昂迭代法结合高效的数值模式匹配法用于感应测井中的反演与剖面成象。首先利用玻昂近拟将非线性问题线性比，然后应用吉洪诺夫正则化与迭代方法求解电磁场的积分方程。     

Inversion of induction tool measurements using the distorted Borniterative method and CG-FFHT

The inversion of induction tool measurements using the distorted Born iterative method (DBIM) and the conjugate gradient-fast Fourier-Hankel transform (CG-FFHT) is described. The inverse problem is formulated in terms of an integral equation of scattering where the unknown to be sought is the conductivity in the rock formation, when the measurements along a borehole axis are performed. The nonlinear problem is linearized at each stage using the distorted Born approximation. The inhomogeneous medium Green's function in the distorted Born approximation is found by solving a volume integral equation using the CG-FFHT method, which allows a rapid solution to a large problem with reduced computational complexity and memory requirement. In this manner, the inverse problem is solved with a computational complexity proportional to N_tlN log N where N_tl is the number of transmitter locations used in the data collection and N is the total number of pixels used to model the unknown formation. The memory requirement is of order NN_tl     

Reconstruction of cylindrically layered media using an iterative algorithm with a stable solution

The reconstruction of cylindrically layered media is investigated in this article. The inverse problem is modeled using a source-type integral equation with a series of cylindrical waves as incidences, and a conventional Born iterative procedure is modified for solving the integral equation. In the modified iterative procedure, a conventional single-point approximation for the calculation of the field inside media is replaced by a multi-points approximation to improve the numerical stability of its solution. Numerical simulations for different permittivity distributions are demon- strated in terms of artificial scattering data with the procedure. The result shows that the procedure enjoys both accuracy and stability in the numerical computation.     

Image reconstruction from TE scattering data using equation ofstrong permittivity fluctuation

Compared to the TM case, the inverse scattering problem for the TE incident field is more complicated due to its stronger nonlinearity. This work provides an effective method for the reconstruction of two-dimensional (2-D) inhomogeneous dielectric objects from TE scattering data. The algorithm applies the distorted Born iterative method to the integral equation of strong permittivity fluctuation to reconstruct scatterers with high-permittivity contrast. Numerical simulations are performed and the results show that the distorted Born iterative method (DBIM) for strong permittivity fluctuation (SPF-DBIM) converges faster and can obtain better reconstructions for objects with larger dimensions and higher contrasts in comparison with ordinary DBIM. A frequency hopping technique is also applied to further increase the contrast     

一阶Born近似下的不均匀目标贝叶斯压缩感知微波成像方法

针对不均匀散射体重构问题,提出了一种基于Born 近似下的贝叶斯压缩感知微波成像方法。在一阶Born 近似框架下,基于电场积分方程并对成像区域网格离散建立稀疏感知模型,然后构造基于高斯先验的贝叶斯概率密度函数,并利用相关向量机方法对目标函数进行优化求解,最终实现对目标的微波成像。通过对多像素单目标、不均匀单目标、不均匀多目标等的微波成像研究并考虑了噪声影响,数值算例结果表明基于高斯先验的贝叶斯压缩感知方法重构结果要优于共轭梯度迭代算法和正交匹配追踪压缩感知重构算法,验证了文中方法的有效性和鲁棒性。     

二维有耗介质目标重建的迭代－共轭梯度方法

本文提出了一种由已知的散射场数据重建二维非均匀有耗目标的复介电常数的迭代算法。连续采用多个方向的ＴＭ平面波照射目标，并分别采集目标区域外的散射场数据。本文利用矩量法．（ＭＯＭ）将积分方程变成矩阵方程，我们以Ｂｏｒｎ近似为初始值，通过多次迭代，实现目标特性的重建。通常，逆问题多是不适定的。为了克服解的不适定性，我们采用共轭梯度法（ＣＧＭ）求解逆问题。最后，通过计算机模拟，给出了一些数值重建结果。     

Iterative numerical computation of the electromagnetic fieldsinside weakly nonlinear infinite dielectric cylinders of arbitrary crosssections using the distorted-wave Born approximation

The electromagnetic scattering by weakly nonlinear infinite dielectric cylinders is the topic dealt with in this paper. The cylinders are assumed to be isotropic, inhomogeneous, and lossless and to have arbitrarily shaped cross sections. A time-periodic illumination of the transverse magnetic type is considered. The nonlinearity is assumed to be expressed by the dependence of the dielectric permittivity on the internal electric field, under the hypothesis that the operator responsible for the nonlinearity does not modify the scalar nature of the dielectric permittivity and produces a time-periodic output. The electromagnetic scattering is then described by an integral equation formulation, and the electromagnetic field distributions inside and outside a scatterer are approximated by an iterative numerical procedure starting with the application of the distorted-wave Born approximation. In a simplified version of the approach, the classic first-order Born approximation is used. The convergence of the approach is discussed in several examples. In the computer simulations concerning cylinders with different cross-section shapes, the effects of the nonlinearity on the field-component fundamental frequency were evaluated for different values of the nonlinear parameters in the case of a Kerr-like nonlinearity and of a uniform incident plane wave. The generation of higher-order harmonics was also considered