基于全变分最小化和交替方向法的康普顿散射成像重建算法

康普顿散射成像技术利用射线与物质作用后的散射光子信息对物质的电子密度进行成像.与传统的透射成像方式相比,康普顿散射成像具有系统结构灵活、成像对比度高、辐射剂量低等优势,在无损检测、医疗诊断、安全检查等领域有着广阔的应用前景.但其重建问题是一个非线性的逆问题,通常是不适定的,其解对噪声和测量误差非常敏感.为解决此问题,本文结合全变分最小化正则化方法和交替方向法提出了一种新的康普顿散射成像重建算法.该算法首先将问题对应的TV模型转化为与之等价的带约束的优化问题,然后利用增广拉格朗日乘子法将优化问题分解为两个具有解析解的子问题,并通过交替求解子问题使增广拉格朗日函数达到最小,进而得到重建的图像.在仿真实验中,通过与主流的ASD-POCS方法进行对比,证明了该算法在重建精度和重建效率方面的优势.     

结合透射CT的康普顿背散射图像重建

在康普顿散射成像(CST)技术中可以结合透射成像重建出衰减系数来消除散射重建的非线性,但这样得到的投影矩阵带有误差。而CST重建问题的不适定性对噪声和投影矩阵的误差非常敏感,重建结果会有较大误差。针对此问题,基于压缩感知理论提出了一种新的CST重建算法。新方法将图像重建问题归结为一个图像的全变分(TV)最小化问题,并使用收敛速度较快的基于交替方向法的Split-Bregman方法进行求解。在仿真实验中,通过与代数重建技术(ART)进行比较,在测量数据充足和测量数据不足两种情况下,本文算法都具有更好的重建质量,证明了所提算法在重建精度和抗噪性能方面的优势。     

对非线性康普顿散射几种改进物理模型的比较

非线性康普顿散射被认为是未来超短超强激光与物质相互作用中的主导性物理过程之一。目前大多数相关研究都基于一种主流的非线性康普顿散射物理模型,该模型假设辐射形成距离足够短、对初态和末态自旋求平均与求和、并忽略了参与散射的激光光子的能动量。近年来,一些研究为了在更广阔的参数空间内,更准确地描述非线性康普顿散射,也对这个主流物理模型提出了几种修正和改进。回顾了对非线性康普顿散射主流物理模型进行的几种改进和修正,介绍了它们的适用范围,分析了它们的基本性质并对其物理效应进行了简单讨论。     

Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model

Optical tomography is a novel imaging modality that is employed to reconstruct cross-sectional images of the optical properties of highly scattering media given measurements performed on the surface of the medium. Recent advances in this field have mainly been driven by biomedical applications in which near-infrared light is used for transillumination and reflectance measurements of highly scattering biological tissues. Many of the reconstruction algorithms currently utilized for optical tomography make use of model-based iterative image reconstruction (MOBIIR) schemes. The imaging problem is formulated as an optimization problem, in which an objective function is minimized. In the simplest case the objective function is a normalized-squared error between measured and predicted data. The predicted data are obtained by using a forward model that describes light propagation in the scattering medium given a certain distribution of optical properties.In part I of this two-part study, we presented a forward model that is based on the time-independent equation of radiative transfer. Using experimental data we showed that this transport-theory-based forward model can accurately predict light propagation in highly scattering media that contain void-like inclusions. In part II we focus on the details of our image reconstruction scheme (inverse model). A crucial component of this scheme involves the efficient and accurate determination of the gradient of the objective function with respect to all optical properties. This calculation is performed using an adjoint differentiation algorithm that allows for fast calculation of this gradient. Having calculated this gradient, we minimize the objective function with a gradient-based optimization method, which results in the reconstruction of the spatial distribution of scattering and absorption coefficients inside the medium. In addition to presenting the mathematical and numerical background of our code, we present reconstruction results based on experimentally obtained data from highly scattering media that contain void-like regions. These types of media play an important role in optical tomographic imaging of the human brain and joints.     

Three-dimensional visualization of objects in scattering medium using integral imaging and spectral analysis

This paper presents a three-dimensional visualization method of 3D objects in a scattering medium. The proposed method employs integral imaging and spectral analysis to improve the visual quality of 3D images. The images observed from 3D objects in the scattering medium such as turbid water suffer from image degradation due to scattering. The main reason is that the observed image signal is very weak compared with the scattering signal. Common image enhancement techniques including histogram equalization and contrast enhancement works improperly to overcome the problem. Thus, integral imaging that enables to integrate the weak signals from multiple images was discussed to improve image quality. In this paper, we apply spectral analysis to an integral imaging system such as the computational integral imaging reconstruction. Also, we introduce a signal model with a visibility parameter to analyze the scattering signal. The proposed method based on spectral analysis efficiently estimates the original signal and it is applied to elemental images. The visibility-enhanced elemental images are then used to reconstruct 3D images using a computational integral imaging reconstruction algorithm. To evaluate the proposed method, we perform the optical experiments for 3D objects in turbid water. The experimental results indicate that the proposed method outperforms the existing methods.     

基于高斯核主成分分析的多通道拉曼光谱重建

针对多通道拉曼成像系统常会受荧光背景、噪声等非线性因素的影响而导致拉曼光谱重建结果一般的问题,提出了一种基于高斯核主成分分析的拉曼光谱重建算法.首先利用相似度因子对标定样本数据集进行预处理,其次通过高斯核函数将标定样本以非线性形式映射至高维特征空间,接着在特征空间中对映射后的数据集提取基函数并通过伪逆法求得与之对应的基函数系数.使用聚甲基丙烯酸甲酯作为测试样本,并引入均方根误差来评估拉曼光谱重建结果的准确性.实验结果表明,相比传统的伪逆法与维纳估计法,该算法具有更高的重建精度及抗噪能力,且能有效降低标定样本中不良数据和成像系统中非线性因素对拉曼光谱重建的影响.因此,该算法可以为多通道拉曼快速成像提供一种有效的拉曼光谱重建算法.     

Compton 散射对线偏光在相对论等离子体中调制不稳定性的影响

应用多光子非线性Compton 散射模型、电磁波非线性色散方程和Karpman 方法,研究了 Compton 散射对线偏光在相对论等离子体中调制不稳定性的影响,给出了等离子体的非线性色散、控制和调制不稳定性增 长率的修正方程,并进行了数值模拟。结果表明：与散射前相比,随无量纲化频率值减小,即趋于等离子体临界面处,散射使相同扰动波数引起的调制不稳定性增长率更大,使等离子体临界面处的调制不稳定性增长率较其余位置尤为显著。这是由于散射光使等离子体非线性增强,形成了激光场自聚焦和自成丝的缘故。     

Compton散射对非均匀等离子体光子晶体光子带隙的影响

应用多光子非线性Compton散射模型和时域有限差分法,对多光子非线性Compton散射对非均匀等离子体光子晶体光子带隙特性的影响进行了研究,提出将入射和散射光作为形成光子带隙的新机制,对电磁波方程进行了修正.结果表明:与Compton散射前相比,散射使电磁波幅值衰减更快|随等离子体密度增加,透射谱禁带宽度几乎无变化,其中心频率向高频方向有明显移动,向上的峰值有较大增加,反射谱向下的峰值有明显减小|随温度增加,透射谱禁带宽明显减小,向上的峰值略有减小,透射能量有所降低|随两种介质介电系数比增加,光子禁带数增加,且带隙间距显著减小.     

Compton ɢ�����ƫ��������۵��������е��Ʋ��ȶ��Ե�Ӱ��

By using the model of multi-photon nonlinear Compton scattering, the nonlinear dispersion relation and Karpman’s model, the influences of the modulation instability on Compton scattering to the linear polarized light in relativistic plasma were studied, the revised equations on the nonlinear dispersion, the control and the growth rate of the modulation instability were given out, and these equations are simulated. The results show that under the same perturbation wave numbers, the even big rate of the modulation instability near the plasma surface are taken place by Compton scattering along with the decreasing of the numbers of the no gauge frequency than before Compton scattering, and the even marked growth rate of the modulation instability near the plasma surface are taken place near the plasma surface than other places. Because the plasma nonlinear is increased by the scattering, the self-focusing and self-turned fine silk are formed.     

三维海洋波导中散射目标快速声学远场成像

研究用声传播远场分布信息成像海洋波导环境中三维散射目标的反问题,提出一种指示器样本成像方法,在不需要预先知道散射目标的任何声学和几何特性的情况下,可以快速得到其位置、形状等几何信息的一个理想的像.数值试验表明,该方法对成像海洋波导中三维散射目标是有效的,即使在有限孔径测量方式和具有噪声测量数据时,也能够得到散射目标的一个理想成像,表明海洋波导边界的多重反射效应对成像效果具有一定的正面影响.     

阵列式康普顿相机GEANT4模拟与图像重建及优化

出于对放射性核素各种应用和安全的考虑,需要性能良好的康普顿相机。通过蒙特卡罗方法模拟了双层阵列式康普顿相机,散射探测器材料为Si,吸收探测器材料为CZT（碲锌镉）。利用反投影图像重建算法进行了图像重建,采用极大似然法对重建结果进行优化,有效地提高了重建图像的分辨率。当放射源与探测器距离100 mm时,经过10次极大似然法迭代计算,位置分辨率与角分辨率分别达到5.1 mm与7.3。检验了极大似然法对于康普顿相机放射源图像重建的优化作用。     

Comptonɢ��Թ����м�������������ź�ǿ�ȹ�ϵ��Ӱ��

应用光声理论、相对论量子理论和电子与多光子集团非线性Compton散射模型,研究了Compton散射对掺杂固体中光声信号强度的影响。结果表明,当掺杂固体中发生电子与多光子集团之间的多光子非线性Compton散射时,在忽略光声转换效率的变化和基质晶格对介电函数贡献的情况下,耦合激光能量和磁感应强度是影响光声信号强度的两个主要因素,其中耦合磁感应强度起主导作用。Compton散射使光声信号强度随耦合光的磁感应强度和能量的增大而迅速增大。能量与光声信号声压之间存在对数线性关系,但它相对于Compton散射前的曲线下移。     

Compton散射对固体中激光能量与光声信号强度关系的影响

应用光声理论、相对论量子理论和电子与多光子集团非线性Compton散射模型,研究了Compton散射对掺杂固体中光声信号强度的影响。结果表明,当掺杂固体中发生电子与多光子集团之间的多光子非线性Compton散射时,在忽略光声转换效率的变化和基质晶格对介电函数贡献的情况下,耦合激光能量和磁感应强度是影响光声信号强度的两个主要因素,其中耦合磁感应强度起主导作用。Compton散射使光声信号强度随耦合光的磁感应强度和能量的增大而迅速增大。能量与光声信号声压之间存在对数线性关系,但它相对于Compton散射前的曲线下移。     

Comptonɢ��Ե��������м���˥�����Ե�Ӱ��

应用多光子非线性Compton散射模型,研究了Compton散射对等离子体中激光衰减特性的影响.提出了Compton散射是影响激光衰减的一个重要机制,给出了激光能量和功率衰减值的表达式,并进行了数值模拟.结果表明,Compton散射对等离子体中传输的激光能量和功率衰减值有较大影响,理论计算和数值模拟符合得很好.这也为判断等离子体中发生Compton散射提供了依据.     

Comptonɢ���ʱ��ǴŻ�����������Ӿ��������Ӱ��

应用多光子非线性Compton散射模型和时域有限差分法,对Compton散射对时变非磁化等离子体光子晶体禁带的影响进行了研究,提出了将多光子非线性Compton散射电磁波和入射电磁波作为等离子体光子晶体产生光子禁带的新机制,给出了电磁场的Maxwell方程组和叠代方程的修正方程,并进行了数值模拟。结果表明,Compton散射使等离子体禁带宽随等离子体上升时间的增大比散射前有明显减小而最后趋于定值,均匀等离子体透射率峰值比线性等离子体增大得更多,利用Compton散射可实现对光子禁带的控制。     

A novel method for non-destructive Compton scatter imaging based on the genetic algorithm

Compton scattering tomography is widely used in numerous applications such as biomedical imaging, nondestructive industrial testing and environmental survey, etc. This paper proposes the use of the genetic algorithm (GA), which utilizes bio-inspired mathematical models, to construct an image of the insides of a test object via the scattered photons, from a voxel within the object. A NaI(Tl) scintillation detector and a 185 MBq ¹³⁷Cs gamma ray source were used in the experimental measurements. The obtained results show that the proposed GA based method performs well in constructing images of objects.     

基于离轴数字全息改善散斑自相关重建效果

针对在成像物体没有超出散射介质记忆效应范围的情况下,提出一种结合数字离轴全息术减少散射介质成像中散斑自相关噪声的方法。当成像目标经过散射介质时,使用自相关技术结合相位恢复算法能够从散斑中重建成像目标。但在实际成像的过程中,为了有效抑制环境噪声和热噪声等对重建效果的影响,设计利用离轴全息中的相移法消除噪声项中静态噪声项的干扰,再利用散斑自相关与相位恢复算法重建去噪后效果更好的成像目标。采用结构相似度对重建效果进行定量评估,仿真结果表明对于给出的成像目标,去噪前后的结构相似度从0.8796提高到0.9875,验证了该方法的有效性。说明所提出的方法能够改善散斑自相关法重建效果。     

Compton Scattering of Attosecond X-Ray Pulses on a Hydrogen Atom

The Compton scattering of attosecond X-ray pulses on a hydrogen atom has been studied theoretically in terms of the spectral angular scattering probability during the action of a pulse. The dependence of scattering on the carrier frequency, pulse duration, and scattering angle has been analyzed. It has been shown that the probability of the process at certain parameters of the problem is a nonlinear function of the pulse duration.     

A measurement-domain adaptive beamforming approach for ultrasound instrument based on distributed compressed sensing: Initial development

High efficient acquisition of the sensor array signals and accurate reconstruction of the backscattering medium are important issues in ultrasound imaging instrument. This paper presents a novel measurement-domain adaptive beamforming approach (MABF) based on distributed compressed sensing (DCS) which seeks to simultaneously measure signals that are each individually sparse in some domain(s) and also mutually correlated with much few measurements under the Nyquist rate. Instead of sampling conventional backscattering signals at the Nyquist rate, few linear projections of the returned signal with random vectors are taken as measurements, which can reduce the amount of samples per channel greatly and makes the real-time transmission of sensor array data possible. Then high resolution ultrasound image is reconstructed from the few measurements of DCS directly by the proposed MABF algorithm without recovering the raw sensor signals with complex convex optimization algorithm. The simulated results show the effectiveness of the proposed method.     

Aberration correction for time-domain ultrasound diffraction tomography

Extensions of a time-domain diffraction tomography method, which reconstructs spatially dependent sound speed variations from far-field time-domain acoustic scattering measurements, are presented and analyzed. The resulting reconstructions are quantitative images with applications including ultrasonic mammography, and can also be considered candidate solutions to the time-domain inverse scattering problem. Here, the linearized time-domain inverse scattering problem is shown to have no general solution for finite signal bandwidth. However, an approximate solution to the linearized problem is constructed using a simple delay-and-sum method analogous to "gold standard" ultrasonic beamforming. The form of this solution suggests that the full nonlinear inverse scattering problem can be approximated by applying appropriate angle- and space-dependent time shifts to the time-domain scattering data; this analogy leads to a general approach to aberration correction. Two related methods for aberration correction are presented: one in which delays are computed from estimates of the medium using an efficient straight-ray approximation, and one in which delays are applied directly to a time-dependent linearized reconstruction. Numerical results indicate that these correction methods achieve substantial quality improvements for imaging of large scatterers. The parametric range of applicability for the time-domain diffraction tomography method is increased by about a factor of 2 by aberration correction.