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A Compton scattering image reconstruction algorithm based on total variation minimization
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作者 李守鹏 王林元 +2 位作者 闫镔 李磊 刘拥军 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第10期563-569,共7页
Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process.... Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process.The reconstruction problem of Compton scattering imaging is the inverse problem to solve electron densities from nonlinear equations,which is ill-posed.This means the solution exhibits instability and sensitivity to noise or erroneous measurements.Using the theory for reconstruction of sparse images,a reconstruction algorithm based on total variation minimization is proposed.The reconstruction problem is described as an optimization problem with nonlinear data-consistency constraint.The simulated results show that the proposed algorithm could reduce reconstruction error and improve image quality,especially when there are not enough measurements. 展开更多
关键词 Compton scattering tomography inverse problem image reconstruction SPARSE total variation
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A SURVEY OF OPEN CAVITY SCATTERING PROBLEMS 被引量:1
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作者 Peijun Li 《Journal of Computational Mathematics》 SCIE CSCD 2018年第1期1-16,共16页
This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military... This paper gives a brief survey of recent developments on mathematical modeling and analysis of the open cavity scattering problems, which arise in diverse scientific areas and have significant industrial and military applications. The scattering problems are studied for the two-dimensional Helmholtz equation corresponding to the transverse magnetic or electric polarization, and the three-dimensional time-harmonic and time-domain Maxwell equations. Since these problems are imposed in open domains, a key step of the analysis is to develop transparent boundary conditions and reformulate them equivalently into boundary value problems in bounded domains. The well-posedness of weak solutions are shown for the associated variational problems by using either the Lax-Milgram theorem or the Fredholm alternative. 展开更多
关键词 Cavity scattering problem Helmholtz equation Maxwell's equations Trans-parent boundary condition variational problem Well-posedness.
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均匀介质中衍射光栅的电磁散射 被引量:2
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作者 孟品超 姜志侠 李延忠 《吉林大学学报(理学版)》 CAS CSCD 北大核心 2012年第6期1151-1155,共5页
考虑均匀介质中衍射光栅电磁散射问题的数学描述形式,通过引入柱面坐标和人工边界条件,给出了衍射光栅散射问题的可行性数学描述,并给出了与散射问题数学模型等价的变分形式.
关键词 衍射光栅 散射问题 变分问题
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光栅衍射实验问题的分析及解决 被引量:2
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作者 孙艳 高源 《大学物理实验》 2021年第5期30-33,50,共5页
通过分析光栅衍射的原理,明确满足光栅方程的实验条件,即光垂直入射到光栅。针对光栅衍射实验中光栅的调节、现象的观测及测量方法等问题,提出相应的解决方案,并从理论和实验两方面说明采取对称测量法的原因。
关键词 光栅衍射 调节问题 对称测量
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超声CT理论与方法综述 被引量:7
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作者 倪文磊 《CT理论与应用研究(中英文)》 2004年第3期50-55,共6页
目的概述超声CT(Computedtomography)理论的发展过程中提出的的一些主要的理论和方法。方法分别对无散射条件下透射型超声CT、反射型超声CT以及衍射断层成像(diffractiontomography)的相关理论的研究目的、基本思想,以及相应的图像重建... 目的概述超声CT(Computedtomography)理论的发展过程中提出的的一些主要的理论和方法。方法分别对无散射条件下透射型超声CT、反射型超声CT以及衍射断层成像(diffractiontomography)的相关理论的研究目的、基本思想,以及相应的图像重建算法做了简要的概述,同时介绍了反散射(inversescattering)问题在超声成像中的应用。结论由于超声传播的复杂性,各种超声CT理论都有其自身的成立条件,从而使得CT理论的应用范围有限。 展开更多
关键词 超声CT 透射型超声CT 反射型超声CT 衍射断层成像 反散射问题 像重建算法
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光栅反散射问题的神经网络方法 被引量:1
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作者 王丹 尹伟石 孟品超 《长春理工大学学报(自然科学版)》 2023年第3期137-142,共6页
针对测量的近场数据来研究光栅形状重构问题,提出了一种基于端对端结构的神经网络方法。该方法是一种循环神经网络,采用序列对序列的方式进行计算。网络模型以近场数据作为输入,以光栅形状参数作为输出,先利用编码端对输入的近场数据进... 针对测量的近场数据来研究光栅形状重构问题,提出了一种基于端对端结构的神经网络方法。该方法是一种循环神经网络,采用序列对序列的方式进行计算。网络模型以近场数据作为输入,以光栅形状参数作为输出,先利用编码端对输入的近场数据进行特征提取,再通过Adam算法更新模型权重,最后使用解码端进行光栅形状参数的反演。此外,模型利用多个门控循环单元从近场数据中提取近场特征,并将该特征引入到解码端中,为反演光栅形状参数提供了更多的特征参考,进一步提高反演效果。数值实验说明该方法可以有效地重构光栅的形状。 展开更多
关键词 光栅反散射问题 神经网络 门控循环单元 长短期记忆神经网络
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A NEW INTEGRAL EQUATION FORMULATION FOR SCATTERING BY PENETRABLE DIFFRACTION GRATINGS
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作者 Ruming Zhang Bo Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2018年第1期110-127,共18页
This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation fo... This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formula- tion is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the NystrSm method for the new integral equation. Nu- merical examples are also shown to illustrate the applicability of the new integral equation formulation. 展开更多
关键词 scattering problem Transmission condition Periodic interface Diffraction gratings Boundary integral equations Helmholtz equation.
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FullApertureReconstruction of theAcoustic Far-Field Pattern from Few Measurements
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作者 Helene Barucq Chokri Bekkey Rabia Djellouli 《Communications in Computational Physics》 SCIE 2012年第2期647-659,共13页
We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation angles.The reconstruction procedure is a multi-step technique that combines a total v... We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation angles.The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion.The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms.We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements. 展开更多
关键词 Acoustic scattering problem limited aperture inverse obstacle problem ill-posed problem total variation Tikhonov regularization Newton method
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