QL-Born迭代法电磁散射计算

积分方程法是多维电磁响应的数值模拟和反演计算的有效方法之一.在线性化散射电磁场积分方程的基础上,采用迭代Born近似法进行了电导率成像反演.针对迭代Born近似法反演依赖初始模型,而QL近似法无需给定初值的特点,提出了两步法(QL-Born迭代法),用QL近似法计算的结果作为Born迭代法的初始模型,避免人为设置初值,并进行了数值实验.     

各向异性介质三维电磁响应模拟的Ho-GEBA算法

本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性. 关键词： 高阶广义扩展Born近似 积分方程 电磁模拟 解析Green函数     

Photon-transport forward model for imaging in turbid media

A photon-transport forward model for image reconstruction in turbid media is derived that treats weak inhomogeneities through a Born approximation of the Boltzmann radiative transfer equation. This model can conveniently replace the commonly used diffusion approximation in optical tomography. An analytical expression of the background Green's function is obtained from the cumulant solution of the Boltzmann equation. Our model provides the correct behavior of photon migration at early times and reduces at long times to the center-moved diffusion approximation. Numerical comparisons between this model and the standard and center-moved diffusion models are presented.     

Hybrid diffusion approximation in highly absorbing media and its effects of source approximation

A modified diffusion approximation model called the hybrid diffusion approximation that can be used for highly absorbing media is investigated. The analytic solution of the hybrid diffusion approximation for reflectance in two-source approximation and steady-state case with extrapolated boundary is obtained. The effects of source approximation on the analytic solution are investigated, and it is validated that two-source approximation in highly absorbing media to describe the optical properties of biological tissue is necessary. Monte Carlo simulation of recovering optical parameters from refiectant data is done with the use of this model. The errors of recovering μ＇s and μ＇s are smaller than 15% for the reduced albedo between 0.77 and 0.5 with the source-detector separation of 0.4-3 mm.     

Three-dimensional electromagnetic nonlinear inversion in layered media by a hybrid diagonal tensor approximation: Stabilized biconjugate gradient fast Fourier transform method

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for radar applications where the object size is comparable to the wavelength. In the first step of this two-step inversion algorithm, the diagonal tensor approximation is used in the Born iterative method. The solution of this approximate inversion is used as an initial guess for the second step in which further inversion is carried out using a distorted Born iterative method. Since the aim of the second step is to improve the accuracy of the inversion, a full-wave solver, the stabilized biconjugate-gradient fast Fourier transform algorithm, is used for forward modelling. The conjugate-gradient method is applied at each inversion iteration to minimize the functional cost. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, makes this method highly efficient. An inversion problem with 32 768 complex unknowns can be solved with 1% relative error by using a simple personal computer. Several numerical experiments for arbitrarily located source and receiver arrays are presented to show the high efficiency and accuracy of the proposed method.     

Three-dimensional electromagnetic nonlinear inversion in layered media by a hybrid diagonal tensor approximation: Stabilized biconjugate gradient fast Fourier transform method

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for radar applications where the object size is comparable to the wavelength. In the first step of this two-step inversion algorithm, the diagonal tensor approximation is used in the Born iterative method. The solution of this approximate inversion is used as an initial guess for the second step in which further inversion is carried out using a distorted Born iterative method. Since the aim of the second step is to improve the accuracy of the inversion, a full-wave solver, the stabilized biconjugate-gradient fast Fourier transform algorithm, is used for forward modelling. The conjugate-gradient method is applied at each inversion iteration to minimize the functional cost. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, makes this method highly efficient. An inversion problem with 32 768 complex unknowns can be solved with 1% relative error by using a simple personal computer. Several numerical experiments for arbitrarily located source and receiver arrays are presented to show the high efficiency and accuracy of the proposed method.     

Distribution of backscattered intensity in the distorted Born approximation: Application to C-band SAR images of woodland

Abstract

The intensity distribution in synthetic aperture radar (SAR) images of woodland is known to depend upon imaging conditions. Whilst phenomenological models can be used to match observed backscatter distributions, a physical model is needed to explain their origins. Images of woodland obtained during airborne SAR trials are analysed and shown to exhibit non-exponential intensity distributions. Expressions are derived for the moments of the intensity distribution using discrete scattering models based on the Born and distorted Born approximations. The predictions of the Born approximation are such that, at all but extremely high resolutions, the intensity statistics reflect only fluctuations in the number of discrete scatterers in resolution cells. In the distorted Born approximation it is revealed that, even at modest resolutions, fluctuations in both number and cross section of objects can influence intensity distributions. This is shown to be a direct consequence of the incorporation of attenuation effects in the distorted Born model. The theory is applied to scattering from a model woodland canopy and shown to yield intensity moments in close agreement with observations. The consequences of the model for other scattering situations are discussed.     

A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging

Emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring, and ultrasonic techniques show promise in this regard. Various tomographic algorithms are available that reconstruct sound speed or contrast profiles, which can be related to temperature distribution. The requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise. In this study, the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated. The transient probing wave field had a bandwidth spanning the frequency range 2.5-320.5 kHz. The results from a forward model which computed the propagation and scattering of low-frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the Born approximation, representing two main types of reconstruction. The first uses Fourier techniques to reconstruct sound-speed profiles from projection or Radon data based on optical ray theory, seen as an asymptotical limit for comparison. The second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory. The results show that the accuracy in localization was 2.5 mm or better when using low frequencies and the conjugate gradient inversion scheme, which could be used for temperature monitoring.     

Transport-based image reconstruction in turbid media with small source-detector separations

We demonstrate a new method for imaging through several millimeters of a turbid sample with a resolution of approximately 100 mum by combining aspects of confocal reflectance microscopy and diffuse optical tomography. By laterally displacing the pinhole aperture of a confocal microscope we can achieve small source-detector separations and detect minimally scattered light. A reconstruction algorithm based on the first Born approximation to the radiative transport equation is then used to reconstruct an image of a 100-mum absorbing object located 2 mm beneath the surface.     

Coupling to an endfaced multi-clad optical fibre from a misaligned gaussian beam or a separated multi-clad fibre

The excitation of a multi-clad optical fibre by a misaligned gaussian beam is analysed using a least-squares boundary residual modal technique and a Born approximation. The modal technique is used to analyse the axial coupling via a gap between two aligned fibres. Comparison is made with a method based on a gaussian approximation for the fibre fields. Results of the modal technique confirm the accuracy of the Born approximation when corrected for Fresnel reflection. However, the modal technique is more precise than the other methods when serious mismatch exists and is efficient for treating the gap problem, where the Born approximation is not applicable.     

基于成像差分吸收光谱技术和压缩感知理论的烟囱烟羽断层重建研究

烟羽断层重建质量受两方面条件限制：其中一个限制条件是遥感设备的时间分辨率。以往的研究多使用多轴差分吸收光谱仪（MAX-DOAS）进行CT重建,受采集数据速度的限制,重建图像的时间分辨率较低。另一个限制条件是,采集到的数据量有限,是典型的不完全角度重建。过去多使用代数迭代重建算法或统计迭代重建算法,重建图像受测量误差的影响比较大,分辨率较低且伪影较多。构造了基于成像差分吸收光谱技术（IDOAS）的光谱数据采集系统,与多轴差分吸收光谱仪构造的系统相比,数据采集的时间分辨率提高了160多倍,基本解决了时间分辨率的问题。提出了一种基于压缩感知理论和低三阶导数模型的烟羽断层重建算法--投影凸函数集低三阶导数法,简称为POCS-LTD。在投影的过程中,使用代数重建算法使重建图像符合投影方程;在全变分迭代的过程中使用了优化算法,将低三阶导数模型的全变分归一化值作为优化算法的迭代方向,前次迭代运算结果与本次投影运算的差值的模作为迭代步长。对重建算法进行了数值模拟,并以重建图像的接近度和一致性相关因子为指标,对重建结果进行了分析。数值模拟表明,算法具有良好的抗误差能力,与传统的低三阶导数法相比,本文提出的算法将重建接近度减小了80%以上。使用烟羽数据采集系统进行了外场实验,用POCS-LTD算法对外场实验的数据进行了烟羽重建,重建图像显示烟羽图像清晰,伪影得到了较好的抑制。介绍的烟羽断层数据采集系统和烟羽断层重建算法,提高了烟羽断层重建图像的时间分辨率,减少了重建图像的伪影,扩大了光谱测量技术的应用范围。     

Phase-coded aperture for optical imaging

For the optical spectrum region, we describe a novel phase-coded aperture imaging system that can be used in a computational imaging camera. The optical design includes a phase-only screen followed by a detector array. A specific diffraction pattern forms at the detector array when the wavefront from a point source object passes through the phase screen. Since diffraction effects cannot be ignored in the optical regime, an iterative phase retrieval method is used to calculate the phase coded screen. Correlation type processing can be applied for the image recovery. Computer simulation results are presented to illustrate the excellent imaging performance of this camera.     

A review of iterative phase retrieval for measurement and encryption

Phase retrieval technique is regarded as one of the most significant tools to solve optical inverse problems. Several phase retrieval algorithms are discussed in this review. The occurrence of ill-posed conditions often makes the calculation difficult. As a synthesis, the multiple-image phase retrieval technology is invented to obtain more accurate convergence result in iterative computation. The multiple-input retrieval scheme can attach new constraints on convergence as a new limitation. As an indirect measuring method, it will make it possible to reconstruct the distribution of intensity and phase in an imaging or measurement system, where data processing is executed by computer. Moreover, the retrieval method has been applied for image encryption successfully. Finally, the development and application of the iterative phase retrieval are overviewed.     

基于模糊度量的激光水下图像复原的盲去卷积方法

由于水体对激光存在着不可克服的吸收和散射效应,距离选通水下激光成像系统所获得的图像存在不同程度的劣化问题,具有信噪比低、边缘模糊等特点.为提高图像质量,将基于模糊度量的盲去卷积方法应用于激光水下成像的图像复原中.结合威尔斯小角度近似得出的点扩展函数与调制传递函数,分别讨论了最大期望,最小均方与多次乘法迭代盲去卷积算法,...     

Image reconstruction in diffuse optical tomography using the coupled radiative transport-diffusion model

The coupled radiative transport-diffusion model can be used as light transport model in situations in which the diffusion equation is not a valid approximation everywhere in the domain. In the coupled model, light propagation is modelled with the radiative transport equation in sub-domains in which the approximations of the diffusion equation are not valid, such as within low-scattering regions, and the diffusion approximation is used elsewhere in the domain. In this paper, an image reconstruction method for diffuse optical tomography based on using the coupled radiative transport-diffusion model is developed. In the approach, absorption and scattering distributions are estimated by minimising a regularised least-squares error between the measured data and solution of the coupled model. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the coupled radiative transport-diffusion model can be utilised in image reconstruction problem of diffuse optical tomography and that it produces as good quality reconstructions as the full radiative transport equation also in the presence of low-scattering regions.     

旁瓣约束下期望主瓣幅度响应迭代波束设计

研究了旁瓣约束下的期望主瓣幅度逼近问题,其包含双边绝对值不等式结构,为非凸波束设计问题。针对传统的多约束优化算法难以处理非凸结构,提出了两种迭代算法。一种对原优化问题作局域线性近似,将非凸约束转换为仿射约束,进而迭代局部二阶锥规划问题求解原问题。另一种通过引入辅助变量构建增广拉格朗日函数,将加权向量与各约束解耦合,交替迭代求解关于原变量、主瓣辅助变量与旁瓣辅助变量的三个子优化问题以给出初始非凸问题的解。针对子优化问题,通过灵活运用拉格朗日乘子技术构建了低复杂度求解方案。采用仿真和实测阵列流形验证设计效果,结果表明,所提两种迭代算法可实现主瓣幅度逼近,合成平顶波束图,且对阵型无依赖性。交替迭代法耗时显著低于迭代二阶锥规划法。      

Non-linear inverse scattering: high resolution quantitative breast tissue tomography

Recent published results in inverse scattering generally show the difficulty in dealing with moderate to high contrast inhomogeneities when employing linearized or iteratively linearized algorithms (e.g., distorted Born iterative method). This paper presents a fully nonlinear algorithm utilizing full wave field data, that results in ultrasound computed tomographic images from a laboratory breast scanner, and shows several such unique images from volunteer subjects. The forward problem, data collection process and inverse scattering algorithm used are discussed. A functional that represents the "best fit" between predicted and measured data is minimized, and therefore requires a very fast forward problem solver, Jacobian calculation, and gradient estimation, all of which are described. The data collection device is described. The algorithm and device yield quantitative estimates of human breast tissue in vivo. Several high resolution images, measuring ～150 by 150 wavelengths, obtained from the 2D inverse scattering algorithms, using data collected from a first prototype, are shown and discussed. The quantitative values are compared with previous published work.     

In vivo biomicroscopy with ultrasound 2

In the first article of this series it was shown that the use of inverse scattering theory to analyse ultrasound reflections could provide high resolution images of the acoustic impedance profile of the retina. Unlike the retina, most tissue structures of interest, like small tumours and arterial plaque deposits, are shielded from view by intervening layers of tissue of appreciable acoustic impedance and attenuation. By analysing a one-dimensional model for a plaque deposit on the wall of a carotid artery embedded in a 5 cm thick layer of tissue, we demonstrate that a relatively high quality image can be recovered when compensation for the attenuation of the intervening tissue is made. We observe that because of the dearth of low frequency power in the recovered signal of ultrasound transducers, it is important that the field of view imaged is not taken to be too large. We compare the exact iterative distorted wave Born approximation inverse scattering method with the approximate but computationally faster plane wave Born approximation method and find that they give images of comparable quality for this model.     

中子与52Cr反应截面的理论分析

根据中子与天然核Cr及其同位素反应的总截面,去弹性散射截面和弹性散射角分布的实验数据,获得了入射中子能量从1MeV—250MeV的一组普适中子与Cr及其同位素反应的光学模型势参数.应用光学模型,扭曲波玻恩近似理论,宽度涨落修正的Hauser-Feshbach理论,和预平衡反应的激子模型,计算和分析了中子与⁵²Cr反应的所有截面、角分布、能谱和双微分截面.理论计算与实验数据进行了分析比较.     

利用阵列多信息对大区域地层电导率的反演

提出利用变形玻恩迭代方法将阵列多信息用于实际大区域地层反演的新方法。该区域是由复杂的过渡带和没受泥浆侵入的原状地层组成的。该方法基于非线性积分方程,用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感应的正演问题。一些数值模拟表明,利用阵列多信息能很好地对复杂地层进行成象,且成象结果与真实电导率剖面分布吻合得比较好。