Electrical impedance tomography: regularized imaging and contrast detection

Dynamic electrical impedance tomography (EIT) images changes in the conductivity distribution of a medium from low frequency electrical measurements made at electrodes on the medium surface. Reconstruction of the conductivity distribution is an under-determined and ill-posed problem, typically requiring either simplifying assumptions or regularization based on a priori knowledge. This paper presents a maximum a posteriori (MAP) approach to linearized image reconstruction using knowledge of the noise variance of the measurements and the covariance of the conductivity distribution. This approach has the advantage of an intuitive interpretation of the algorithm parameters as well as fast (near real time) image reconstruction. In order to compare this approach to existing algorithms, the authors develop figures of merit to measure the reconstructed image resolution, the noise amplification of the image reconstruction, and the fidelity of positioning in the image. Finally, the authors develop a communications systems approach to calculate the probability of detection of a conductivity contrast in the reconstructed image as a function of the measurement noise and the reconstruction algorithm used.     

A Novel Finite-Element-Based Algorithm for Fluorescence Molecular Tomography of Heterogeneous Media

The knowledge of optical properties distribution of heterogeneous media has significant impact on the reconstructed fluorescence image quality in fluorescence molecular tomography (FMT). In this study, a novel finite-element-based algorithm for FMT of heterogeneous media is proposed. In the algorithm, optical properties are reconstructed using the conjugate gradient method. A modified method based on reverse differential scheme is deduced for calculating the gradient when the detector points are not restricted on boundary nodes. With the recovered optical properties, linear relationship between known surface measurements of emission light and unknown fluorescence yield is then obtained. FMT reconstruction is implemented by combining algebraic reconstruction technique (ART) and Landweber iteration method. With initial value provided by ART, Landweber iteration method improves the quantification smoothly with small step length between neighboring iterations. The algorithm was evaluated using phantoms of different heterogeneity configurations. Results show that the reconstructed fluorescence yield is insensitive to various degrees of heterogeneity for the proposed algorithm. In contrast, when assuming homogeneous optical properties, it shows that more underestimation of optical properties results in more underestimation of the reconstructed fluorescence yield. Fast computation speed of the proposed algorithm is also demonstrated in this study.     

An interior point iterative maximum-likelihood reconstruction algorithm incorporating upper and lower bounds with application to SPECT transmission imaging

The algorithm we consider here is a block-iterative (or ordered subset) version of the interior point algorithm for transmission reconstruction. Our algorithm is an interior point method because each vector of the iterative sequence [x(k)], k = 0, 1, 2, ... satisfies the constraints a(j) < x(j)k < b(j), j = 1, ..., J. Because it is a block-iterative algorithm that reconstructs the transmission attenuation map and places constraints above and below the pixel values of the reconstructed image, we call it the BITAB method. Computer simulations using the three-dimensional mathematical cardiac and torso phantom, reveal that the BITAB algorithm in conjunction with reasonably selected prior upper and lower bounds has the potential to improve the accuracy of the reconstructed attenuation coefficients from truncated fan beam transmission projections. By suitably selecting the bounds, it is possible to restrict the over estimation of coefficients outside the fully sampled region, that results from reconstructing truncated fan beam projections with iterative transmission algorithms such as the maximum-likelihood gradient type algorithm.     

增广拉格朗日双边全变分压缩成像重构算法

针对基于全变分压缩成像算法重构的图像存在虚假边界以及边缘信息对比度低的问题,提出了一种基于全变分成像模型的增广拉格朗日双边全变分压缩成像重构算法。在全变分正则化思想基础上引入双边滤波技术,并加入拉格朗日函数算子,将目标函数转化为增广拉格朗日函数,利用交替方向法求解函数模型的最优解。迭代过程中选用最速下降法对梯度进行求解,对算法进行优化,提高算法运行速度。实验结果表明,算法改进后可以更加精确的重构出原始图像,重构图像的峰值信噪比提高2 dB,重构错误率降低10%,结构相似度提高0.1,并且对噪声具有较好的鲁棒性。     

高图像配准精度的非相干数字全息彩色成像

菲涅耳非相干相关全息是一种能记录非相干物体全息图的新型技术,在生物医学成像和三维遥感领域具有重要应用前景。针对高光谱成像过程中图像融合配准困难的问题,文中利用空间光调制器的可编程特性,设计并制作了波长分别为492、562、672 nm的三组焦距恒定的双透镜相位掩模,依次调用三种波长的掩模并记录对应波长下物体的全息图。由于三色记录光经对应波长掩模调制后在CCD表面汇聚的光斑位置及尺寸均相同,因此,全息图重建后获得的重建图像具有相同的横向放大率,可提高图像融合时的配准精度,免去繁杂的光谱图像空间配准算法,真正实现了全息彩色成像的高精度配准和实时融合。采用该系统记录骰子的全息图,经数值重建及色彩融合后得到了颜色重建性较好的彩色三维像。     

多准则图象重建的神经网络模型及实现

本文提出一种采用Ｈｏｐｆｉｅｌｅ神经网络（Ｈｏｐｆｉｅｌｄ Ｎｅｉｒａｌ Ｎｅｔｗｏｒｋ简称ＨＮＮ）优化的图象重建算法。将图象重建问题转化为ＨＮＮ优化问题,取重建图象的峰值函数最小以及原始投影与再投影之间的误差平方和最小作为图象重建的优化目标,作为能量函数构造连续型ＨＮＮ模型,由ＨＮＮ能量函数极小化可得到重建问题的优化解。这种方法具有简单、计算量小、收敛快、便于并行计算等特点。对照ＡＲＴ算法,用计算机模拟产生的无噪声投影数据检验新算法,验证了新算法的优越性。     

Electromagnetic impedance tomography (EMIT): a new method for impedance imaging

We propose a new impedance imaging method, electromagnetic impedance tomography (EMIT), in which the boundary electric potential measurements in electrical impedance tomography (EIT) are augmented by measurements of the exterior magnetic field induced by the currents excited in the object by the standard EIT procedures. These magnetic measurements can be obtained reliably and inexpensively by simple pickup coils located around the imaged cross section. We derive expressions for the forward problem and for the Jacobian of the measurements, and propose an iterative reconstruction algorithm using a squared error cost function. The performance of EMIT and EIT is compared in numerical simulations using a finite-element model for the conductivity distribution of several phantoms. Evaluation of the rank and condition of the Jacobian demonstrates that the additional magnetic measurements provided by a few pickup coils in EMIT turn an underdetermined EIT problem into a well-posed one with reasonable condition, or significantly improve the conditioning of the EIT problem when it is already fully determined. Reconstructions of various phantoms reveal that EMIT provides particularly significant visual and quantitative improvement (threefold to tenfold reduction in the root-mean-squared error) in the sensitivity at the center of the object, which is the area most difficult to image using EIT.     

Nonlinear multigrid algorithms for Bayesian optical diffusiontomography

Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem. Bayesian approaches are effective, but are computationally expensive, especially for three-dimensional (3-D) imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical diffusion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality     

基于强度调制的编码孔径光谱偏振测量方法

为实现在单次成像条件下获取图像的光谱偏振信息,提出了一种基于强度调制的编码孔径测量方法。该方法采用消色差1/4波片、多级相位延迟器和检偏器组成的光谱偏振强度调制模块,将入射光的Stokes参量各元素谱调制到不同的频率上,利用编码孔径和色散棱镜组成的光谱成像系统对该调制光谱进行压缩编码,并通过CCD进行探测。利用TwIST算法重构出经调制的光谱信息,对各个频谱通道进行分离重构出Stokes元素谱。以单一像素点为例,对入射光强度调制、光谱重构及Stokes参量的解调进行了数值模拟。结果表明:该方法可实现对稀疏图像的光谱偏振信息的获取,该过程仅需对图像进行一次测量,因此具备高速获取能力。     

压缩感知重构算法在“鬼”成像中的应用研究

“鬼”成像（GI）提供了一种用常规手段很难达到的特殊的获取图像方法,在量子光学领域是近些年来的前沿和热点之一。本文中,主要研究压缩感知（CS）的重构算法在“鬼”成像中的应用。我们使用具有高斯分布的热光源强度分布,来作为压缩感知的测量矩阵,分别以离散余弦变换(DCT)和离散小波变换(DWT)作为压缩感知中图像物体的稀疏矩阵,利用正交匹配追踪算法,最终获得基于压缩感知重构算法的“鬼”成像。研究结果表明,压缩比为0.5时,基于离散余弦变换基的压缩“鬼”成像（DCT-CS）和基于小波变换基的压缩“鬼”成像(DWT-CS),比“鬼”成像原始重建算法有超过10dB的峰值信噪比提升;同时,基于DCT-CS算法的重建质量要优于DWT-CS算法。      

一种约束最小模方估计的图像迭代重建算法

较少投影重建问题一直是成像领域研究的重点，传统的卷积反投影(CBP)不能产生满意的重建图像——伪影严重、误差大，而迭代算法却具有一些较好的特性。本文以CT成像为基础，以最小模方为目标函数提出了一种约束迭代重建算法，本算法与无约束迭代算法相比，在花费相同时间的情况下，可以重建出误差更小，拟合度更高的图像。以扇束扫描投影数据重建的结果验证了本文的结论。     

用于光子计数单像素成像的去块状采样网络

将光子计数技术和单像素成像结合,能实现高灵敏、低成本的光子计数成像,但存在采样时间和重建时间长的问题。基于深度学习的压缩采样和重建网络,将去除偏置和激活函数的全连接层作为测量矩阵,通过从数据中学得高效的测量矩阵和避免传统迭代算法带来的巨大计算量,实现了更快、更高质量的图像重建。但利用全连接层进行高分辨图像的分块压缩感知时,重建图像会产生块状效应。针对该问题提出了重叠分块采样网络（Os_net）、嵌套采样网络(Ns_net)、卷积采样网络（Cs_net）等三种方法以取代全连接层采样。在重建网络的设计中,使用线性映射网络对图像进行重建,设计实验结果表明Cs_net的去块状化效果最好。将Cs_net二值化后应用于光子计数单像素成像系统,实验结果表明Cs_net除块状化明显优于传统算法TVAL3,且Cs_net在重建质量上也同样取得了较好的效果。     

基于相位调制的运动目标多光谱关联成像研究

为克服扫描方式多光谱成像无法捕获动态场景下的多光谱数据,提出了一种基于相位调制实现运动目标单次曝光多光谱成像方法。该方法将关联成像技术、压缩感知技术与光谱成像相结合,在成像光路中引入空间随机相位调制器,对运动目标物体三维图谱信息数据进行调制和压缩,然后利用探测器获取二维混叠信号,实现单次曝光获取运动目标的三维图谱信息重构,具有光能利用率高、成像时间短、系统结构简单等优点。实验结果表明:单帧CCD探测信号的电子数均值从200 e?按100 e?的间隔增加到1300 e?时,随着电子数均值增加,重构图像相对均方根误差rRMSE值对应减小,重构图像质量提高;当步进电机以30 Hz速度带动目标物体连续运动时,可获得较好质量运动物体的多光谱重构图像;采用光谱仪对目标物体中不同谱段的光谱分布曲线进行测试,所得结果与重构图像的光谱分布曲线相吻合,证明了该方法的有效性。研究结果对多光谱关联成像技术在无人机平台、动态监测等领域的应用提供了有益借鉴。     

信号压缩与重构的交替方向外点持续法

针对压缩感知（Compressed Sensing,CS）中信号重构的l1-正则化问题中的l1-正则项非光滑,求解比较困难,提出了交替方向外点持续法（Alternating Direction Exterior Point Continuation Method,ADEPCM）.该算法首先将信号的稀疏域的l1-正则化问题通过变量分裂（Variable Splitting,VS）技术转化为与之等价的约束优化问题;然后采用一步Gauss-Seidel思想,对优化问题中的变量最小化,并采用持续的思想更新罚参数,重构出信号的稀疏系数;最后进行正交反变换,重构出原始信号.并将ADEPCM用于图像重构,进行了仿真实验及对实验结果进行了分析.实验结果表明：与现有的一些重构算法相比,ADEPCM具有稍高的峰值信噪比（Peak Signal to Noise Ratio,PSNR）和更快速的收敛速度.     

High-resolution NMR chemical-shift imaging with reconstruction by the chirp z-transform

A study of a novel nuclear magnetic resonance (NMR) chemical-shift image reconstruction method with a high chemical-shift resolution achieved by the chirp z-transform (CZT) is presented. Phase encoding is used for the spatial coordinates x and y, and the frequency coordinate is reserved especially for the chemical shift. The Fourier transform (FT) image reconstruction algorithm, which forms the basis of the new CZT image reconstruction method, is introduced. The novel method, using the CZT instead of the FT to evaluate the chemical-shift spectrum at a much higher resolution, is studied. The chemical-shift resolutions, achieved by the FT and the CZT, are studied theoretically from the aspect of the peak height and the peak width of chemical-shift spectra. The chemical-shift spectra calculated at a selected point in the image plane, and the chemical shift-images reconstructed by this method, are shown for a simple phantom containing ethanol and methanol at different locations. The results obtained by this method and by the FT method are compared and discussed. The experimental results have shown that a chemical-shift as small as 39 Hz, relative to the proton resonance frequency of 21.34 MHz, can be resolved successfully by this method without improvements in magnetic field homogeneity.     

Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media

A three-dimensional image reconstruction for fluorescence-enhanced frequency-domain photon migration (FDPM) measurements in turbid media is developed and investigated for three different simulated measurement types: 1) absolute emission measurement, or emission measurements of phase and amplitude attenuation made for a given incident point source of excitation light; 2) referenced emission measurements made relative to an excitation measurement conducted at a single reference point away from the incident source; and 3) referenced emission measurements made relative to the excitation measurement conducted at identical points of detection. The image reconstruction algorithm employs a gradient-based constrained truncated Newton (CONTN) method which implements a bounding parameter, which can be used to govern the level of contrast used to discriminate tissue volumes from heterogeneous background tissues. Reverse differentiation technique is used to calculate the gradients. Using simulated data with superimposed noise to achieve a signal-to-noise ratio of 55 and 35 dB to mimic experimental excitation and emission FDPM measurements, respectively, we show the robustness of emission measurements referenced to excitation light. We investigate the performance of algorithm CONTN using these measurement techniques and show that the absorption coefficients due to fluorophore are reconstructed by CONTN accurately and efficiently. Furthermore, we demonstrate the performance of the bounding parameter for rejection of background artifacts owing to background tissue heterogeneity.     

基于ARTUR算法的气动光学效应图像校正方法

提出了一种基于ARTUR算法的气动光学效应图像校正方法。该方法利用一些合理的先验知识对大气扰动退化模型(点扩展函数)进行规化,将求解问题转化为带惩罚项的准则函数的优化估计问题,通过ARTUR算法快速迭代估计点扩展函数值,进而对气动光学效应引起的退化图像进行校正。论述了ARTUR算法的性质,给出了实验结果。     

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted /spl lscr//sup 1/ and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.     

基于频率选择表面的毫米波压缩感知成像

基于频率选择表面,提出了一种毫米波压缩感知成像方法。通过在频率选择表面单元中加载开关二极管,并随机控制它们处于开/关状态,设计了一种可随机切换的新型毫米波成像掩膜板。通过将这种随机掩膜板放置于毫米波天线上,能够构造出相应的随机测量矩阵并获取足够多的有效测量次数。利用恢复重构算法进行了成像仿真验证,结果证实了所提方法的可行性。     

基于全变差的加权最小二乘法PET图像重建

传统的加权最小二乘法、惩罚项加权最小二乘法虽然能够重建得到较好质量的图像,但在欠采样的条件下不能很好的拟制噪声.全变差作为正则项已广泛用于图像重建中,利用图像稀疏的先验知识能够在欠采样的条件下很好的重建图像.本文结合加权最小二乘法和全变差的优点,构造了基于全变差正则项的加权最小二乘法目标函数,运用交替求解的方法,将目标函数分解为求解二次优化和全变差正则化的优化问题,并分别用超松弛迭代方法和梯度下降法求解这两个优化问题.采用Zubal模型对该算法与传统算法进行仿真验证比较,并用相关系数、方差、信噪比等参数描述图像重建质量.结果表明在欠采样条件下,该算法能够更好的拟制噪声,重构效果比传统的有明显地提高.