基于统计反演的硅片微区电阻率测试方法

提出了一种基于统计反演重建电阻率分布图像的硅片电阻率测试方法，该方法采用马尔科夫链蒙特卡洛(MCMC)方法求解电阻抗成像技术(EIT)的逆问题，可以避免确定性方法中迭代误差和分辨率低的问题。建立了一种基于MCMC方法的电阻率分布图像重建算法，搭建了电压数据采集系统以测量边缘电压。对比MCMC算法重建的硅片微区电阻率分布图像与4D-333A测试仪的测量结果，二者的电阻率分布情况呈现出相同的分布趋势。将采用MCMC算法得出的256个单元的数值与采用其他重建方法得出的数值、真实的电阻率进行对比，发现MCMC算法得到的数值与真实数值最接近的单元数最多，为88个，比其他重建方法更为准确。     

基于截断奇异值的镜像综合孔径亮温重建方法

镜像综合孔径(MAS)辐射计的图像重建是由余弦可见度函数到场景亮温的图像反演过程,余弦可见度函数由转移方程求解得到.而转移方程为不适定方程组,相关输出中一个较小的误差,都可能引起求解的余弦可见度函数存在较大偏离.因此,对这个不适定方程组的求解是整个亮温重建算法成功的关键.该文基于镜像综合孔径的基本原理,分析转移矩阵的病...     

基于截断奇异值的镜像综合孔径亮温重建方法

镜像综合孔径(MAS)辐射计的图像重建是由余弦可见度函数到场景亮温的图像反演过程,余弦可见度函数由转移方程求解得到.而转移方程为不适定方程组,相关输出中一个较小的误差,都可能引起求解的余弦可见度函数存在较大偏离.因此,对这个不适定方程组的求解是整个亮温重建算法成功的关键.该文基于镜像综合孔径的基本原理,分析转移矩阵的病态性,将截断奇异值分解应用于转移方程的求解问题中.仿真与实验表明,该方法可以有效降低噪声,提升图像质量.     

基于混合共轭梯度的SAR图像压缩感知重建

近年来，压缩感知已广泛用于合成孔径雷达(SAR)图像、医学图像重建和磁共振成像等图像处理领域。传统平滑l₀范数(SL0)重建方法通过引入平滑函数，很好地将求解最小l₀范数这个NP-hard问题转化成求解平滑函数极值的凸优化问题，但SL0方法使用最速下降法搜索最优解，存在锯齿效应、收敛速度不理想的问题。为了解决上述问题，文中首先定义了一种新的混合共轭梯度；然后，在研究SL0方法的基础上，提出了一种新的基于混合共轭梯度的改进SL0压缩感知重建方法。实验表明：文中所提方法收敛速度快，对噪声不敏感，具有较好的稳健性；在相同实验条件下，对SAR图像的重建性能优于SL0和其他同类方法，重建质量更好。     

一种时变三维电离层CT算法

提出了利用GPS观测数据获得时变三维电离层电子密度分布的一种CT反演算法。对GPS地面接收台网的合理布设进行了初步的尝试，在此基础上，利用实际的GPS射线路径和通过IRI90模式计算得到的TEC进行了模拟反演，得到了电子密度在一小时内随时间、空间变化的图像。通过与IRI90模式直接得到的电子密度分布图像进行比较，证明该算法能重现原始模型中的特征，其重建质量较好。     

多基地SAR线目标参数反演与图像重建

传统单基地SAR成像系统基于点目标模型且观测视角单一,在对复杂场景成像时存在线目标边缘不连续,特征丢失等现象。针对这一问题,本文提出了一种多基地SAR构型下线目标参数反演与图像重建方法。该方法基于几何模型与散射理论推导了线目标的合成孔径雷达回波的参数化表达式,分析了在不同观测角度下对线目标的SAR成像结果从直线段到两端点反复变化的特点,并从空间谱采样的角度解释了这一现象,在此基础上根据线目标空间谱的特征,提出了一种基于最小二乘估计的多基地构型下线目标参数反演与图像重建方法。仿真实验结果表明,在相同的峰值信噪比条件下,本文提出的多基地SAR线目标参数反演与图像重建方法,相对于单一观测角度的单基地SAR具有更优的反演性能,在SAR图像的峰值信噪比为28dB时,线目标朝向与长度的反演误差在10％以内的概率达到了84％,可以基于反演结果实现图像的重建。      

基于广义低秩矩阵分解的分离字典训练及其快速重建算法

针对传统压缩感知重建算法存在重建质量偏低、重建时间偏长等问题,本文提出了一种基于分离字典训练的快速重建算法.首先选取某类图像作为训练集,建立其广义低秩矩阵分解模型;其次采用交替方向乘子法求解该模型,训练出一组分离字典;最后将该分离字典用于图像重建中,通过简单的线性运算实现图像的快速重建.实验结果表明,本文算法相比于传统的重建算法,针对训练集同类图像,具有十分显著的重建性能,对于其他不同类型的图像,依然有不错的重建质量,极大地降低了重建时间.     

基于压缩感知理论的高能闪光照相密度反演方法

高能闪光照相中需要研究少数投影数据条件下的非轴对称客体的的密度反演问题。现有利用压缩感知思想的全变差TV类算法虽然考虑了图像的局部相似性，但没有考虑图像的非局部相似性。针对上述问题，文中提出了一种基于组稀疏正则化的全变分重建技术TV-GSR。该技术将组稀疏模型集成于TV框架之下，同时考虑了客体图像的局部相似性和非局部自相似性，充分利用了图像的先验稀疏信息，并利用客体的上、下、左、右4点对称性来降低图像重建的规模，重构精度有所增加，重建速度也更快。仿真实验表明，文中提出的TV-GSR算法提升了图像在无噪声和有噪声情况下的重建精度，对于高能闪光图像和纹理细节丰富的CT图像都有较好的效果，具有普适性。     

电容层析成像的电场分布与反演

通过分析等势线及电容敏感场分布,深入探讨了电容层析成像电场分布的"软场"特性及导致反演问题非线性、不适定的机理.提出一个基于三层B-P神经网络的图像重建算法.网络的输入是预处理过的电容矢量,输出直接对应到空间图像.实验结果表明,该算法成像速度快且精度高,较以前的成像算法有很大的改进.     

基于探地雷达首达时约束的层状构造波形反演方法

采用现有的方法对层状构造探地雷达数据进行波形反演时,存在两个难题：问题求解过程时间复杂度高和误差分析函数收敛性差。为了解决这些问题,提出一种基于首达时约束的波形反演方法,该方法以各层介质分界面处对应的回波信号的首达时为先验信息,以降低算法求解过程的复杂度,并保证误差分析函数的收敛性。实验结果表明：针对层状构造反演问题,改进后的波形反演方法能有效重建出各层介质的厚度和介电常数信息;同时,该方法还具有时间复杂度低和反演结果精度高等优点。     

Mask design for optical microlithography--an inverse imaging problem.

In all imaging systems, the forward process introduces undesirable effects that cause the output signal to be a distorted version of the input. A typical example is of course the blur introduced by the aperture. When the input to such systems can be controlled, prewarping techniques can be employed which consist of systematically modifying the input such that it (at least approximately) cancels out (or compensates for) the process losses. In this paper, we focus on the optical proximity correction mask design problem for "optical microlithography," a process similar to photographic printing used for transferring binary circuit patterns onto silicon wafers. We consider the idealized case of an incoherent imaging system and solve an inverse problem which is an approximation of the real-world optical lithography problem. Our algorithm is based on pixel-based mask representation and uses a continuous function formulation. We also employ the regularization framework to control the tone and complexity of the synthesized masks. Finally, we discuss the extension of our framework to coherent and (the more practical) partially coherent imaging systems.     

Mask Design for Optical Microlithography—An Inverse Imaging Problem

In all imaging systems, the forward process introduces undesirable effects that cause the output signal to be a distorted version of the input. A typical example is of course the blur introduced by the aperture. When the input to such systems can be controlled, prewarping techniques can be employed which consist of systematically modifying the input such that it (at least approximately) cancels out (or compensates for) the process losses. In this paper, we focus on the optical proximity correction mask design problem for "optical microlithography," a process similar to photographic printing used for transferring binary circuit patterns onto silicon wafers. We consider the idealized case of an incoherent imaging system and solve an inverse problem which is an approximation of the real-world optical lithography problem. Our algorithm is based on pixel-based mask representation and uses a continuous function formulation. We also employ the regularization framework to control the tone and complexity of the synthesized masks. Finally, we discuss the extension of our framework to coherent and (the more practical) partially coherent imaging systems     

Discretization Error Analysis and Adaptive Meshing Algorithms for Fluorescence Diffuse Optical Tomography: Part I

For imaging problems in which numerical solutions need to be computed for both the inverse and the underlying forward problems, discretization can be a major factor that determines the accuracy of imaging. In this work, we analyze the effect of discretization on the accuracy of fluorescence diffuse optical tomography. We model the forward problem by a pair of diffusion equations at the excitation and emission wavelengths and consider a finite element discretization method for the numerical solution of the forward problem. For the inverse problem, we use an optimization framework which allows incorporation of a priori information in the form of zeroth- and first-order Tikhonov regularization terms. Next, we convert the inverse problem into a variational problem and use Galerkin projection to discretize the inverse problem. Following the discretization, we analyze the error in reconstructed images due to the discretization of the forward and inverse problems and present two theorems which point out the factors that may lead to high error such as the mutual dependence of the forward and inverse problems, the number of sources and detectors, their configuration and their positions with respect to fluorophore concentration, and the formulation of the inverse problem. Finally, we demonstrate the results and implications of our error analysis by numerical experiments. In the second part of the paper, we apply our results to design novel adaptive discretization algorithms.      

Task-based comparison of inverse methods in magnetoencephalography

Magnetoencephalography (MEG) provides unique insights into the spatio-temporal dynamics of neural activation in the human brain. Unfortunately, the accuracy with which neural sources can be localized is limited by the highly illposed nature of the inverse problem. A large number of inverse methods have been proposed that deal with this illposedness using a range of different modeling and regularization procedures. Here we describe an objective task-based framework for comparing different inverse methods. Using the free-response receiver operating characteristic (FROC) we compare the performance of matched filters, cortically constrained dipole scanning, and minimum norm imaging methods for the task of detecting focal cortical activation. Our results indicate that the scanning methods outperform matched filters and minimum norm imaging for the case of one and two 2 cm2 patches of cortical activity when the dynamics of the two patches are both strongly and weakly correlated and irrespective of the spacing of the two activated regions.     

A narrow-band level set method applied to EIT in brain for cryosurgery monitoring

In this paper, we investigate the feasibility of applying a novel level set reconstruction technique to electrical imaging of the human brain. We focus particularly on the potential application of electrical impedance tomography (EIT) to cryosurgery monitoring. In this application, cancerous tissue is treated by a local freezing technique using a small needle-like cryosurgery probe. The interface between frozen and nonfrozen tissue can be expected to have a relatively high contrast in conductivity and we treat the inverse problem of locating and monitoring this interface during the treatment. A level set method is used as a powerful and flexible tool for tracking the propagating interfaces during the monitoring process. For calculating sensitivities and the Jacobian when deforming the interfaces we employ an adjoint formula rather than a direct differentiation technique. In particular, we are using a narrow-band technique for this procedure. This combination of an adjoint technique and a narrow-band technique for calculating Jacobians results in a computationally efficient and extremely fast method for solving the inverse problem. Moreover, due to the reduced number of unknowns in each step of the narrow-band approach compared to a pixel- or voxel-based technique, our reconstruction scheme tends to be much more stable. We demonstrate that our new method also outperforms its pixel-/voxel-based counterparts in terms of image quality in this application.     

Data Specific Spatially Varying Regularization for Multimodal Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) allows in vivo localization and quantification of fluorescence biodistributions in whole animals. The ill-posed nature of the tomographic reconstruction problem, however, limits the attainable resolution. Improvements in resolution and overall imaging performance can be achieved by forming image priors from geometric information obtained by a secondary anatomical or functional high-resolution imaging modality such as X-ray computed tomography or magnetic resonance imaging. A particular challenge in using image priors is to avoid the use of assumptions that may bias the solution and reduced the accuracy of the inverse problem. This is particularly relevant in FMT inversions where there is not an evident link between secondary geometric information and the underlying fluorescence biodistribution. We present here a new, two step approach to incorporating structural priors into the FMT inverse problem. By using the anatomic information to define a low dimensional inverse problem, we obtain a solution which we then use to determine the parameters defining a spatially varying regularization matrix for the full resolution problem. The regularization term is thus customized for each data set and is guided by the data rather than depending only on user defined a priori assumptions. Results are presented for both simulated and experimental data sets, and show significant improvements in image quality as compared to traditional regularization techniques.      

A general framework for nonlinear multigrid inversion.

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction is particularly difficult because the forward problem is both nonlinear and computationally expensive to evaluate. In this paper, we propose a general framework for nonlinear multigrid inversion that is applicable to a wide variety of inverse problems. The multigrid inversion algorithm results from the application of recursive multigrid techniques to the solution of optimization problems arising from inverse problems. The method works by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid inversion algorithm efficiently computes the solution to the desired fine-scale inversion problem. Importantly, the new algorithm can greatly reduce computation because both the forward and inverse problems are more coarsely discretized at lower resolutions. An application of our method to Bayesian optical diffusion tomography with a generalized Gaussian Markov random-field image prior model shows the potential for very large computational savings. Numerical data also indicates robust convergence with a range of initialization conditions for this nonconvex optimization problem.     

Image recovery from Fourier domain measurements via classification using Bayesian approach and total variation regularization

In this paper we propose a Potts–Markov prior and total variation regularization associated with Bayesian approach to simultaneously reconstruct and segment piecewise homogeneous images in Fourier synthesis inverse problem. When the observed data do not fill uniformly the Fourier domain which is the case in many applications in tomographic imaging, or when the phase of the signal is lacking as in optical interferometry the results obtained by deterministic methods are not satisfactory. Such inverse problem is known to be nonlinear and ill-posed. It then needs to be regularized by introducing prior information. The particular a priori information on which we rely is the fact that the image is composed of a different regions finite known number. Such an appropriate modeling of the image gives the possibility of compensating the lack of information in the data thus giving satisfactory results. We define the appropriate Potts–Markov model to define parameters of label regions for such images and total variation to be used in a Bayesian estimation framework.     

基于深度学习的复杂沙漠背景SAR目标检测

SAR目标检测,因成像场景大、背景复杂多变而极具挑战。传统基于恒虚警率的SAR目标检测方法极易受背景干扰。针对上述问题,提出一种基于深度学习的复杂沙漠背景SAR目标端对端检测识别系统。即采用小规模沙漠背景下的SAR图像数据对Faster-RCNN网络进行迁移训练,一体化完成典型目标的检测与识别。基于合成数据集Desert-SAR的试验结果表明,与传统方法相比,该方法检测速度更快、准确率更高、鲁棒性更强。     

光学医学成像实验技术综述：II—间接成像法

光学医学成像方法可分为两大类,即直接法和间接法。对于厘米级以上的软组织,由于早期到达光的比例极小,因此在安全曝光量下直接法是不现实的。目前广泛流行的间接法则利用全部可探测到的光能,通过求解特定光子模型的逆向问题实现图像的重建,是有望实现临床光学医学成像的方法之一。本文综述了近红外光辐射医学成像研究中间接成像法所涉及的实验技术。