Through-Wall Imaging via a Linear Inverse Scattering Algorithm

A through-wall imaging problem for a 2-D scalar geometry is addressed. It is cast as an inverse scattering problem and tackled under the linear model of the electromagnetic scattering that is provided by the Born approximation. A truncated singular value decomposition inversion scheme is exploited, and the performances that are achievable by such an inversion scheme are assessed by exploiting synthetic data. The cases of weakly and strongly scattering objects are both considered. Finally, an example of reconstruction that is obtained by exploiting experimental data is presented.     

New tools and series for forward and inverse scattering problems in lossy media

A convenient rewriting of the pertinent integral equation is exploited to introduce a new model for two-dimensional electromagnetic scattering by dielectric objects in lossy media. Exploiting this latter, a new series expansion is introduced to solve the forward problem accurately and effectively. The first term of such a series coincides, in particular situations, with the well-known extended Born approximation. Theoretical tools and results are given on the range of applicability and rate of convergence of the series, which favorably compares with the traditional Born one. These tools allow noticing that the new model exhibits a lower "degree of nonlinearity" with respect to parameters embedding dielectric characteristics as compared to the traditional model, thus suggesting its exploitation in the solution of the inverse problem. Numerical examples assessing effectiveness and convenience of the proposed models, tools and inversion methods are presented.     

A novel effective model for solving 3-D nonlinear inverse scattering problems in lossy scenarios

A proper extension of the contrast source extended Born model, recently introduced in the two-dimensional scalar case, is proposed to establish a novel full-wave inversion method for nonlinear vectorial three-dimensional scattering problems. In particular, a suitable auxiliary function, embedding the parameters of the unknown targets, is introduced as fundamental unknown of the inverse problem instead of the widely used contrast function. Numerical examples confirm effectiveness and reliability of the proposed inversion approach, which also favorably compares with other methods previously known in the literature.     

Three-Dimensional Microwave Tomography by a 2-D Slice-Based Reconstruction Algorithm

This letter deals with the problem of imaging 3-D strong scatterers by means of a 2-D slice tomographic reconstruction algorithm. More in detail, the inversion algorithm is based on two steps. In the first step, 2-D slices of the object are reconstructed; then, they are superimposed and interpolated to achieve the 3-D representation of the object. The Kirchhoff approximation is exploited to develop a linear inversion scheme for reconstructing the 2-D slices for scatterers embedded in the free space. Finally, the inversion algorithm is checked against synthetic data for the interesting case of scatterers resembling the human body.     

动态大地测量反演及其在地震非均匀破裂研究中的应用

本文从固体力学基本方程出发,提出了一类反问题,将其定义为动态大地测量反问题,运用有限元法和正则化方法研究了动态大地测量反问题的解和性质,提出了动态大地测量反演的正则化方法;最后,讨论了动态大地测量反演在地震非均匀破裂研究中的应用,利用大地测量资料反演获得了唐山地震的非均匀破裂图像。     

Application of an Inexact-Newton Method Within the Second-Order Born Approximation to Buried Objects

The imaging of buried objects is a challenging topic in electromagnetic research. In this letter, a method previously proposed for imaging of scatterers in free-space is extended to the case of objects buried in a lossy half-space. The proposed approach is based on the solution of the underlying inverse-scattering problem within the second-order Born approximation by means of a two-step inexact-Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations. Furthermore, comparisons with the free-space approach are also reported     

Three-Dimensional ISAR Imaging Using a Two-Dimensional Sparse Antenna Array

Conventional antenna array 3-D inverse synthetic aperture radar (ISAR) imaging method does imaging by first carrying out ISAR imaging for all the different antennas and then using array direction of arrival (DOA) estimation on every scatterer to get the position of that scatterer. The aperture formed by the target's motion is used to separate the scatterers, and the antenna array aperture is used for position measurement. In this letter, a 3-D imaging method based on a combination of sparse array beamforming and ISAR imaging is proposed, where 3-D images are formed by space-time match filtering. The estimation of the target's rotation parameters is also given. Simulation results have shown the effectiveness of the proposed methods.      

基于力学模式的动态大地测量数据反演研究

本文在文献（１）的基础上，进一步研究了基于力学模式动态大地测量反演理论。首先提出了力学模式下动态大地测量反问题的六种形式，导出了第一，二类动态大地测量反问题的线性最小的二乘解，研究了动态大地测量反问题的妥；最后，结合数值例子，讨论了利用地壳垂直形变数据反演地壳断层错动的一种方法。     

基于χ2准则的磁梯度张量3D聚焦反演方法

针对铁磁性物质反演中正则化参数自适应选择的问题,提出了基于χ2准则的磁梯度张量3D聚焦反演方法。利用深度加权矩阵和最小支撑矩阵对经典Tikhonov正则化理论框架下的反演模型进行约束得到目标函数,避免了由于反演参数多于采集点数而导致反演解的多解性,并有效解决了核函数随深度增大而快速衰减的问题。通过对目标函数进行迭代奇异值分解获得最佳物性参数,并根据χ2准则自适应地确定目标函数在迭代过程中的正则化参数,提高了迭代速度和求解精度。仿真和实验结果表明:该方法能准确还原磁性异常体的轮廓形态,具有较好的模型分辨率。     

大地测量联合反演理论和方法研究进展

综述了10多年来国内外大地测量反演问题研究的成果及最新进展，特别是大地测量联合反演模型、大地测量联合反演算法以及大地测量联合反演理论和方法在研究地壳运动、地球构造等中的应用成果，讨论了联合卫星测高、声纳测深及海洋激光雷达遥感信息反演海洋环境参量，联合INSAR、GPS和水准资料反演研究地壳运动和联合各种观测数据反演研究地球内部构造问题。随着科学技术的发展，大地测量联合反演理论和方法研究将在监测全球变化、防灾减灾、发展地球科学理论方面取得更大进展。     

原子Na的电子碰撞电离

使用Ｒ矩阵方法, 在扭曲波和库仑玻恩近似下计算了入射电子能量为２０ ｅＶ、５０ｅＶ 及１００ ｅＶ 原子Ｎａ 的电子碰撞电离截面, 并详细给出了入射电子能量为５０ ｅＶ 时的能量微分截面及分波能量微分截面。计算结果揭示了明显的Ｒｙｄｅｒｇ 系列共振, 并使用量子亏损理论对结果进行分析和讨论, 展示了Ｒｙｄｅｒｇ 系列共振的丰富内容。     

利用航空重力梯度反演Kauring试验场三维密度结构

相对于传统的重力测量手段,重力梯度测量能够以更高的灵敏度和分辨能力反映出地下密度异常体的结构特征。由于拉格朗日经验参数在实测数据反演中存在不确定性,对预条件共轭梯度反演算法加以改进,利用L曲线的拐点值代替原反演算法中的拉格朗日经验参数作为正则化参数;为改善反演中存在的病态性问题并减弱核函数的快速衰减,将地下模型改进为不等间隔模型;为改善反演中解的非唯一性,利用重力梯度的5个独立分量进行联合反演;通过对澳大利亚Kauring试验场航空重力梯度张量进行联合反演,得到该地区异常体的三维密度分布,将重力梯度联合反演结果与之前的重力反演结果对比分析,发现在中心异常体附近沿线还分布着多个异常块体。结果表明,改进后的算法能够有效地利用实测重力梯度数据反演出密度异常体的分布信息。     

自主海洋测高卫星串飞模式的设计与重力场反演精度分析

根据自主海洋测高卫星发展需求,设计了双星串飞运行模式,该运行模式下2.3 a时间可满足全球海洋区域1'×1'分辨率的地面轨迹覆盖要求。首先,将测高卫星重力场反演分为不考虑轨道运行特点（思路1）和考虑串飞轨道运行特点（思路2）两种思路,利用逆Vening-Meinesz方法开展了正态分布下随机误差传播的仿真计算,获得了两种思路下对应的误差指标。以该误差指标为基础,分别计算了双星串飞模式下两种重力场反演思路对应的精度指标。其中,反演思路2充分利用了串飞模式双星东西方向地面观测值可以进行相对定轨的特点,并考虑到近距离条件下传播误差、地球物理改正误差的系统误差特性,因此反演思路2的垂线偏差精度较反演思路1有了一定的提高,其重力场反演也具有一定的优势。理论计算结果表明,利用思路1的反演方法,2.3 a时间可获得1'×1'重力异常精度为6~10 mGal,4.6 a时间可达到4.2~7.1 mGal;利用思路2的反演方法,2.3 a时间可获得1'×1'重力异常精度为3.9 mGal,4.6 a时间可达到2.8 mGal。     

利用组合算法反演球体分层模型的断层参数

随着空间大地测量观测精度的提高,大地测量反演模型也更加精确细化,对反演算法也提出了更高的要求。针对球体分层位错模型断层参数反演问题,从反演参数的敏感性与相关性两个方面入手,分析了遗传算法在反演中的缺陷,提出了迭代最小二乘算法与遗传算法相结合的组合算法,利用模拟数据反演验证了算法的有效性。在遗传算法的断层参数反演中,断层的深度和滑距往往难以得到良好的结果,主要原因首先是上深度与下深度之间以及深度与滑距之间具有很强的相关性,其次是深度和滑距的敏感性相对来说也比较低。组合算法在各种倾角的断层上都取得了理想的反演结果,具有实用性。     

Reconstruction of One-Dimensional Dielectric Scatterers Using Differential Evolution and Particle Swarm Optimization

A comparison between differential evolution (DE) and particle swarm optimization (PSO) in solving 1-D small-scale inverse scattering problems is presented. In this comparison, the efficiency of both aforementioned optimization techniques is examined for permittivity and conductivity profile reconstruction problems. The comparison is carried out under the same conditions of initial population of candidate solutions and number of iterations. Numerical results indicate that both optimization methods are reliable tools for inverse scattering applications even when noisy measurements are considered. In the particular case of small-scale problems investigated in this letter, DE outperforms the PSO in terms of reconstruction accuracy. This is considered an indicative result and not generally applicable.     

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.     

动态大地测量反演理论及其苦干应用

本文从固体力学基本方程出发，提出了动态大地测量反问题。运用有限元法和正则化方法建立了动态大地测量反演的基本理论，研究了动态大地测量反问题的解和性质，提出了动态大地测量反演的正则化方法。最后给出了利用动态大地测量数据反演岩石弹性模量、区域边界力和断层滑动量的一般方法。     

Robust estimation of deformation from observation differences for free control networks

Deformation measurements have a repeatable nature. This means that deformation measurements are performed often with the same equipment, methods, geometric conditions and in a similar environment in epochs 1 and 2 (e.g., a fully automated, continuous control measurements). It is, therefore, reasonable to assume that the results of deformation measurements can be distorted by both random errors and by some non-random errors, which are constant in both epochs. In other words, there is a high probability that the difference in the accuracy and precision of measurement of the same geometric element of the network in both epochs has a constant value and sign. The constant errors are understood, but the manifestation of these errors is difficult to determine in practice. For free control networks (the group of potential reference points in absolute control networks or the group of potential stable points in relative networks), the results of deformation measurements are most often processed using robust methods. Classical robust methods do not completely eliminate the effect of constant errors. This paper proposes a new robust alternative method called REDOD. The performed tests showed that if the results of deformation measurements were additionally distorted by constant errors, the REDOD method completely eliminated their effect from deformation analysis results. If the results of deformation measurements are only distorted by random errors, the REDOD method yields very similar deformation analysis results as the classical IWST method. The numerical tests were preceded by a theoretical part. The theoretical part describes the algorithm of classical robust methods. Particular attention was paid to the IWST method. In relation to classical robust methods, the optimization problem of the new REDOD method was formulated and the algorithm for its solution was derived.     

正则化滤波在反演地表光谱反照率中的应用

利用有限的卫星观测数据,通过反演地物二向性反射分布函数(BRDF)模型提取复杂地表的真实信息,是一个不适定的地球科学反演问题。为了克服离散不适定性带来的困难,在分析引起模型解不稳定的原因和数据误差传递机制的基础上,使用构建滤波函数的方法实现BRDF模型的正则化约束反演。实验结果表明,正则化滤波算法与MODIS AMBRALS算法精度相当,完全适用于具有充足观测和稀疏观测情况下的地物参数反演。