基于L曲线法的超声CT正则化参数优化

超声逆散射成像图像重建反问题常常是不适定的。此种情况下,仅使用最小二乘法不能保证获得满意的介质分布图像重建结果,因此使用Tikhonov和TSVD正则化算法来产生适当的解。正则化参数的合适选取对图像重建至关重要,其对重建质量和计算速度都有影响,本文采用L-曲线准则确定相应的正则化参数。经实验验证:基于L-曲线法可以快速找到最优正则化参数,TSVD法与Tikhonov正则化方法相比,提高了图像重建质量,且适用范围广。     

On a limited-view reconstruction problem in diffraction tomography

Diffraction tomography (DT) is an inversion technique that reconstructs the refractive index distribution of a scattering object. We previously demonstrated that by exploiting the redundant information in the DT data, the scattering object could be exactly reconstructed using measurements taken over the angular range [0, phimin], where pi < phimin < or = 3pi/2. In this paper, we reveal a relationship between the maximum scanning angle and image resolution when a filtered backpropagation (FBPP) reconstruction algorithm is employed for image reconstruction. Based on this observation, we develop short-scan FBPP algorithms that reconstruct a low-pass filtered scattering object from measurements acquired over the angular range [0, phi(c)], where phi(c) < phimin.     

复参数最大熵图像重建的剑桥算法

本文将正实参数的最大熵图像重建的剑桥算法推广到复参数，此算法能较好的地恢复复参数“图像”。文中还给出了此算法在逆散射成像中应用的计算机模拟实验结果。     

埋于介质体中二维导体目标成象的迭代方法

本文应用一种迭代方法实现了埋于二维均匀介质体中理想导体目标几何构形的重建。在导出介质体与导体混合目标散射边界积分方程的基础上，利用Ｎｅｗｔｏｎ－Ｋａｎｔｏｒｏｖｉｃｈ方法和矩量法建立逆散射基本方程。为克服病态问题，连续采用多方面ＴＭ平面波照射目标以获取足够的信息，并通过迭代方法求解。最后、给出的一些散射目标的重建结果表明本方法的可行性，同时研究了噪声对重建结果的影响。     

Bayesian Image Reconstruction for Improving Detection Performance of Muon Tomography

Muon tomography is a novel technology that is being developed for detecting high-Z materials in vehicles or cargo containers. Maximum likelihood methods have been developed for reconstructing the scattering density image from muon measurements. However, the instability of maximum likelihood estimation often results in noisy images and low detectability of high-Z targets. In this paper, we propose using regularization to improve the image quality of muon tomography. We formulate the muon reconstruction problem in a Bayesian framework by introducing a prior distribution on scattering density images. An iterative shrinkage algorithm is derived to maximize the log posterior distribution. At each iteration, the algorithm obtains the maximum a posteriori update by shrinking an unregularized maximum likelihood update. Inverse quadratic shrinkage functions are derived for generalized Laplacian priors and inverse cubic shrinkage functions are derived for generalized Gaussian priors. Receiver operating characteristic studies using simulated data demonstrate that the Bayesian reconstruction can greatly improve the detection performance of muon tomography.     

An inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique

A shape reconstruction method for electromagnetic tomography based on contour deformations by means of a level set method is proposed. The level set method adds quite valuable features to the inverse procedure such as natural regularization of the contours and automatic breaking and merging capability. The frequency hopping technique turns out to be a key point of the inverse scattering procedure. The numerical results clearly indicate that the use of this inversion algorithm yields to accurate reconstructions of one or several objects from one initial guess object, even with noise-contaminated data and limited coverage of the fields.     

Electromagnetic inverse scattering of two-dimensional perfectlyconducting objects by real-coded genetic algorithm

Shape reconstruction of two-dimensional perfectly conducting objects using noisy measured scattering data is considered. The contour of each conducting object is denoted by a shape function in the local polar coordinate which is approximated by a trigonometric series. A point-matching method is used to solve the scattering problem. The main idea of the inversion algorithm is to cast the inverse problem into a restrained minimization problem and to solve it by the real-coded genetic algorithm (RGA). The performance of this algorithm is demonstrated by numerically reconstructing arbitrarily shaped objects and by a detailed comparison with both the standard genetic algorithm (SGA) and the Newton-Kantorovitch method     

Application of eliminating zero-order diffraction light in wavefront reconstruction of inverse diffraction computation

With the development of computer and CCD tech-niques ,a technique of capturing the complex amplitudeof object light accordingto anintensity holographrecor-ded by a CCD detector array has been becoming an in-teresting area[1-4].In reference [5] the frequen…     

静态阻抗断层图像重建新方法

阻抗断层图像重建是一个严重病态的非线性的逆问题,特别是在静态阻抗断层成像中,由于其图像重建模型误差和测量噪声的影响更为严重,因此常用的基于目标函数梯度信息不断迭代的改进的Newton-Raphson类重建算法,即使使用正则化技术,其稳定性仍较差,甚至发散.本文提出一种全新的静态阻抗断层图像重建方法,它利用基于生物自然选择与遗传机理的遗传算法去搜索阻抗图像重建问题的最优解,无需正则化技术,也不会象改进的Newton-Raphson类算法那样易陷入局部最优解.实验结果也表明基于遗传算法的图像重建方法重建的静态阻抗断层图像,其成像精度和空间分辨率都大大好于改进的Newton-Raphson类重建算法.     

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。     

基于先验信息和正则化技术的图像复原算法的研究

在湍流退化图像复原研究中,为了消除大气湍流的影响,提出了一种基于先验信息和正则化技术的盲解卷积图像复原算法.该算法是以极大似然估计为基本原理,将目标图像和点扩展函数的先验信息以惩罚项的形式引入到极大似然函数中,同时利用正则化技术优化目标图像和点扩展函数的估计过程,以增加极大似然估计算法的收敛性和稳定性.通过退化图像的复原实验结果表明,该算法在退化模型完全未知的情况下,可以有效的实现对湍流退化图像的盲复原.     

基于并行BP神经网络的近红外光断层图像重建方法基础研究

提出一种基于并行BP神经网络的近红外光断层成像(Near-infrared optical tomography,NIR OT)图像重建算法,利用BP神经网络来表征生物组织内部光学参数的空间分布和边界光强之间的非线性映射关系.该方法将一个复杂的模型分解成简单的模型分别建立并行的神经网络.利用Femlab软件完成基于有限元的稳态扩散方程的两个简单模型的正向问题求解,根据提出的平均优化散射系数和正向问题训练的大量数据集合,建立并训练并行神经网络,通过对两个网络结果的分析,实现快速获得更复杂模型的光学参数的重构.算法能够快速识别特异组织的位置和准确反映热疗过程中生物组织的优化散射系数的变化趋势.     

Application of maximum likelihood estimation to radar imaging

An efficient maximum likelihood (ML) estimator to obtain the scattering center locations of a target and the relative scattering level of these scattering centers from the scattered field data is described. In the proposed method, ML estimation is carried out in the image domain rather than in the frequency-aspect domain. A two-dimensional (2-D) inverse Fourier transform is used to transfer the scattered field data from frequency-aspect domain to the image domain (down-range/cross-range). As expected, the scattered field data in the image domain has some regions with high energy. The samples in the high-energy regions are used to obtain the initial guess for the ML estimator as well as for ML estimation. The ML estimator in the image domain is applied to both simulated and experimental scattered fields of some targets     

A matched-filter-based reverse-time migration algorithm forground-penetrating radar data

Ground-penetrating radar (GPR) is a remote sensing technique used to obtain information on subsurface features from data collected over the surface. The process of collecting data may be viewed as mapping from the object space to an image space. Since most GPRs use broad beam width antennas, the energy reflected from a buried structure is recorded over a large lateral aperture in the image spare, migration algorithms are used to reconstruct an accurate scattering map by refocusing the recorded scattering events to their true spatial locations through a backpropagation process. The goal of this paper is to present a pair of finite-difference time-domain (FDTD) reverse-time migration algorithms for GPR data processing. Linear inverse scattering theory is used to develop a matched-filter response for the GPR problem. The reverse-time migration algorithms, developed for both bistatic and monostatic antenna configurations, are implemented via FDTD in the object space. Several examples are presented     

基于DSM-CSI的非线性逆散射算法研究

由于反演问题中散射体所处区域和散射体个数信息的缺失,进而导致非线性逆散射方法的待重构空间维数高和运算代价高。基于线性逆散射方法在重构目标区域和目标个数信息的计算代价低,本文提出一种DSM（Di-rect Sampling Method）线性方法和CSI（Contrast Source Inversion）非线性方法相结合的非线性逆散射方法。该方法利用DSM方法的重构结果为CSI方法提供散射体所处区域和散射体个数的先验信息,进而降低待重构空间的维数以及非线性逆散射问题的计算量。实验计算结果证明了该方法的有效性。     

Stochastic geometrical modeling for built-up area understanding from a single SAR intensity image with meter resolution

To investigate the limits and merits of information extraction from a single high-resolution synthetic aperture radar (SAR) backscatter image, we introduce a model-based algorithm for the automatic reconstruction of building areas from single-observation meter-resolution SAR intensity data. The reconstruction is based on the maximum a posteriori estimation by Monte Carlo methods of an optimal scene that is modeled as a set of mutually interacting Poisson-distributed marked points describing parametric building objects. Each of the objects can be hierarchically decomposed into a collection of radiometrically and geometrically specified object facets that in turn get mapped into data features by ground-to-range projection and inverse Gaussian statistics. The detection of the facets is based on a likelihood ratio. Results are presented for airborne data with resolutions in the range of 0.5-2 m on urban scenes covering agglomerations of buildings. To achieve robust results for building reconstruction, the integration with data from other sources is needed.     

Inverse scattering of dielectric cylinders by a cascaded TE-TMmethod

A novel approach for inverse scattering of dielectric objects Is proposed. This reconstruction algorithm aims to synthesize individual TE and TM inverse scattering in order to decrease the effect of ill-posedness. The proposed synthesizing method has a cascade structure composed of TE and TM inverse scattering algorithms. Appropriate approaches are adopted in these two algorithms to take advantage of the physical difference between them. A diversity scheme of multiple incident views and receiving points is also incorporated. Numerical simulations are conducted to compare the proposed synthesizing method with two other methods using individual TE or TM information. Some advantages of the synthesizing method are also observed     

Study of resolution and super resolution in electromagnetic imaging for half-space problems

It has been observed that super resolution is possible in the electromagnetic imaging. In the first part of the paper, the possible resolution of image is investigated in the inversion of far-field data using the diffraction tomographic (DT) algorithm, where two cases are considered when the object is in a homogeneous space and in an air-earth half space. The study shows that the resolution of image for inversion of far-field data has been limited theoretically to 0.3536-0.5 wavelength using the DT algorithm in homogeneous-space problems, and it is even worse in half-space problems. If the transmitters and receivers are located in the near-field regime, however, the image resolution is less than 0.25 wavelength, which is the super-resolution phenomenon. In the second part of the paper, the physical reason for the super-resolution phenomenon is investigated using different electromagnetic inverse scattering methods. The study has demonstrated that the information of evanescent waves in the measurement data and its involvement in inversion algorithms is the main reason for the super resolution. Four inversion algorithms are considered for half-space problems: the DT algorithm, the spatial-domain Born approximation (BA), the Born iterative method (BIM), and the distorted BIM (DBIM). The first two belong to linear inverse scattering, while the last two belong to nonlinear inverse scattering. Further analysis shows that DBIM provides a better super resolution than BIM, and BIM provides a better super resolution than BA. Numerical simulations validate the above conclusions.     

Microwave Subsurface Imaging Using Direct Finite-Difference Frequency-Domain-Based Inversion

We have developed a new algorithm for electromagnetic inverse scattering problems in inhomogeneous media using finite-difference frequency-domain (FDFD) forward modeling, referred to as the FDFD-based inversion method. The key issue of this method is to build a linear expression for the inverse problem from an FDFD forward model by using Born approximation to neglect mutual coupling between scattered pixels and to then solve for the inverse coefficient matrix. An important advantage of this matrix-based method is that there is no need to specify a Green's function. As such, this inverse scattering algorithm is easily implemented and is robust to the heterogeneity in the background. We test the algorithm with a microwave subsurface object detection application using cross-well radar. The new method is compared with conventional inversion using Green's function-based Born approximation. Numerical experiments are presented for a 2-D borehole geometry for buried object detection in uniform soil and in multilayered soil backgrounds.