融合结构先验信息的稳态扩散光学断层成像重建算法研究

扩散光学断层成像作为一种无辐射损伤、低成本的光学在体成像技术,有着良好的应用前景,但具有空间分辨率低、难以定量的缺陷.为了提高扩散光学断层成像的分辨率,实现光学参数分布的精确重建,基于有限元方法,提出了融合结构先验信息的稳态扩散光学断层成像重建算法.该算法以扩散近似作为成像模型,通过软先验的Laplace 正则化方法引入由MicroCT提供的空间结构信息.采用伴随法计算Jacobian矩阵,Levenberg-Marquardt方法用来进行迭代优化.仿真结果表明该算法不仅能获得精确的光学参数值分布,而且显著地提高了迭代收敛的速度.     

快速多极边界元法用于扩散光学断层成像研究

在求解扩散光学断层成像中的正向问题时, 目前普遍采用有限元法, 但是随着实际模型规模的增大, 有限元法的计算量问题日益显著, 而边界元法则由于可以降低计算维度使计算量减少而备受关注. 本文以均匀的高散射介质为模型, 研究了将快速多极边界元法用于扩散光学断层成像的正向问题. 快速多极边界元法利用核函数的多极展开, 将常规边界元法中系数矩阵和迭代矢量的乘积项等价为相应四叉树结构的一次递归, 再结合广义最小残量法进行迭代求解. 将计算结果和蒙特卡罗法的模拟结果进行了比较, 表明利用快速多极边界元法的模拟结果和蒙特卡罗法的结果有很好的一致性. 研究结果验证了快速多极边界元法可以用于扩散光学断层成像, 为其大规模和实时成像带来可观的前景. 关键词： 扩散光学断层成像 边界元法 快速多极边界元法     

Light propagation for time-domain fluorescence diffuse optical tomography by convolution using lifetime function

Time-domain light propagation in biological tissue is studied by solving the forward problem for fluorescence diffuse optical tomography using a convolution of the zero-lifetime emission light and the exponential function for a finite lifetime. We firstly formulate the fundamental equations in a time-domain assuming that the fluorescence lifetime is equal to zero, and then the solution including the lifetime is obtained by convolving the emission light and the lifetime function. The model is a two-dimensional (2-D) 10 mm-radius circle with the optical properties simulating biological tissue for the near infrared light, and contains some inclusions with fluorophores. Temporal and spatial profiles of excitation and emission light are calculated and discussed for several models with different inclusions. The results are physically reasonable and will be used for the inverse problem of fluorescence diffuse optical tomography.     

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.     

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x-and y-axis directions are obtained with a phaseshifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

A method for phase reconstruction in the optical three-dimensional shape measurement

In the optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid the phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing the numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

A Compton scattering image reconstruction algorithm based on total variation minimization

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.     

Finite element approximation of the Fokker-Planck equation for diffuse optical tomography

In diffuse optical tomography, light transport theory is used to describe photon propagation inside turbid medium. A commonly used simplification for the radiative transport equation is the diffusion approximation due to computational feasibility. However, it is known that the diffusion approximation is not valid close to the sources and boundary and in low-scattering regions. Fokker-Planck equation describes light propagation when scattering is forward-peaked. In this article a numerical solution of the Fokker-Planck equation using finite element method is developed. Approach is validated against Monte Carlo simulation and compared with the diffusion approximation. The results show that the Fokker-Planck equation gives equal or better results than the diffusion approximation on the boundary of a homogeneous medium and in turbid medium containing a low-scattering region when scattering is forward-peaked.     

An algorithm for computed tomography image reconstruction from limited-view projections

<正>With the development of the compressive sensing theory,the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology.This paper develops an iterative algorithm for image reconstruction,which can fit most cases.This method gives an image reconstruction flow with the difference image vector,which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough.Then the l_2-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles.The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data.Moreover,all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.     

PITRE: software for phase‐sensitive X‐ray image processing and tomography reconstruction

Synchrotron‐radiation computed tomography has been applied in many research fields. Here, PITRE (Phase‐sensitive X‐ray Image processing and Tomography REconstruction) and PITRE_BM (PITRE Batch Manager) are presented. PITRE supports phase retrieval for propagation‐based phase‐contrast imaging/tomography (PPCI/PPCT), extracts apparent absorption, refractive and scattering information of diffraction enhanced imaging (DEI), and allows parallel‐beam tomography reconstruction for conventional absorption CT data and for PPCT phase retrieved and DEI‐CT extracted information. PITRE_BM is a batch processing manager for PITRE: it executes a series of tasks, created viaPITRE, without manual intervention. Both PITRE and PITRE_BM are coded in Interactive Data Language (IDL), and have a user‐friendly graphical user interface. They are freeware and can run on Microsoft Windows systems via IDL Virtual Machine, which can be downloaded for free and does not require a license. The data‐processing principle and some examples of application will be presented.     

Two-dimensional optical coherence tomography for real-time structural dynamical characterization

We present a two-dimensional optical coherence vibration tomography (2DOCVT) system with an ultra-precision displacement resolution of ~0.1 nm that is capable of in site real-time absolute displacement measurement of structural line vibrations. Experimental results of sinusoidal, sweep and impulse vibrations were reported. The key figures of merit such as the 2DOCVT system could obtain fast line vibration measurement without scanning and it also could be used to capture structural modal parameters in one single impulse excitation measurement without any vibration excitation input information, making it attractive for the application in low-frequency vibration measurement and response-only modal analysis.     

Reconstruction method for samples with refractive index discontinuities in optical diffraction tomography

We present a reconstruction method for samples containing localized refractive index (RI) discontinuities in optical diffraction tomography. Abrupt RI changes induce regional phase perturbations and random spikes, which will be expanded and strengthened by existing tomographic algorithms, resulting in contaminated reconstructions. This method avoids the disturbance by recognition and separation of the discontinuous regions, and recombination of individually reconstructed data. Three-dimensional RI distributions of two fusion spliced optical fibers with different typical discontinuities are demonstrated, showing distinctly detailed structures of the samples as well as the positions and estimated shapes of the discontinuities.     

基于光学原理的三维形貌测量技术研究

为了加快产品开发和保证产品制造质量需要对物体的三维形貌进行精确的测量。光学形貌测量技术由于其高分辨率、无破坏、数据获取速度快等优点而被认为是最有前途的三维形貌测量方法。介绍了各种基于光学原理的三维形貌测量技术,并作了比较深入的分析和对比,为正确和广泛应用三维形貌测量技术提供了参考。给出了在该领域的发展方向和研究热点。     

A priori information in a regularized sinogram‐based method for removing ring artefacts in tomography

Ring artefacts in X‐ray computerized tomography reconstructions are considered. The authors propose a ring artefact removal method based on a priori information regarding the sinogram including smoothness along the horizontal coordinate, symmetry of the first and the final rows and consideration of small perturbations during acquisition. The method does not require prior reconstruction of the original or corrected sinograms. Its numerical implementation is based on quadratic programming. Its efficacy is examined with regard to experimental data sets collected on graphite and bone.     

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.     

Point-based integration for 3D object reconstruction from Ladar range images

A method of point-based integration from multiple registered laser radar (Ladar) range images for 3D object reconstruction is presented in this literature. Our method operates surface point data directly and provides a direct way for overlapping data removal. The overlapping areas were detected using a single distance threshold. In order to set the distance threshold, a local point density approach is introduced to solve it. Compared with the mesh-based, volumetric and other points-based integration approaches, our method is simple and fast, and need less storage memory. The approach is performed on various objects with different geometric shapes. The experimental results demonstrate the efficiency and feasibility of our method.     

3D shape reconstruction of teeth by shadow speckle correlation method

This paper presents a new method for 3D shape reconstruction in computer-aided dental prosthetics. A specklegram is projected onto the tooth to be measured. This shadow speckle image is recorded and then processed by a digital image correlation method, which enables the computation of 2D shapes based on the similar principle of shadow moiré method. By repeating the procedure for all the sides, i.e., one crown and several side surfaces, local 2D shapes can be measured precisely. Afterwards, these local 2D profiles are merged to form a 3D model, during which certain constraints such as the widths along perpendicular directions are introduced to guide the process. As the height information within an entire image field is recorded instantly, it has the potential to be employed in an intra-oral environment, which would make the patient feel more comfortable during the restoration process. In vitro experiments were carried out on gypsum teeth models and the results proved the effectiveness of the proposed method.     

定量光声层析成像的研究进展

光声层析(Photoacoustic tomography,PAT)成像结合了超声成像的高分辨率和光学成像的高对比度的优势,是一种新型的生物医学成像模式。PAT成像算法包含两个逆问题,即根据组织产生的光声信号构建初始声压分布图(即图像重建)以及在此基础上估算成像区域的光学特性参数。后者是一个非线性的不适定问题,通常称为定量光声层析(Quantitative photo-acoustic tomography,q PAT)成像。本文在介绍光声成像原理的基础上,对主要的q PAT算法进行综述,讨论各自的优势和不足,并对未来可能的发展方向进行展望。     

利用普通光学显微镜实现对微小物体三维体表参数的测量

基于有较大的焦深的普通光学显微镜及3D成像软件,利用自制的可绕固定轴的升降平台及光纤辐照形态,根据视差原理构建了一个测量小型样品的三维表面参数的测试系统。以外形较复杂的医用牙科钻头为样品,研究了显微镜的放大倍数、用于构建三维图像的两幅相似图像的夹角与样品表面参数测量值之间的关系。通过与样品的标称值对比,实验中所用的毫米量级的样品,在合适的物镜组放大倍数及合适的夹角下,相对误差在5%范围内,表明所建立的测量系统可用于尺寸较小的样品表面参数的测量。     

基于约束共轭梯度的高能闪光照相3维重建算法

 针对高能闪光照相系统成像信噪比低的特点,提出了3维约束共轭梯度算法,该算法基于3维重建理论来重建方程,利用约束共轭梯度法迭代求图像重建的最优解。数值模拟结果表明：采用3维约束共轭梯度算法能有效改善高能闪光照相重建图像轴线噪声大的问题,是一种具有很高抗噪能力的闪光照相图像重建算法。