Sparse Bayesian reconstruction method for multispectral bioluminescence tomography

We present a sparse Bayesian reconstruction method based on multiple types of a priori information for multispectral bioluminescence tomography （BLT）. In the Bayesian approach, five kinds of a priori information are incorporated, reducing the ill-posedness of BLT. Specifically, source sparsity characteristic is considered to promote reconstruction results. Considering the computational burden in the multispectral case, a series of strategies is adopted to improve computational efficiency, such as optimal permissible source region strategy and node model of the finite element method. The performance of the proposed algorithm is validated by a heterogeneous three-dimensional （3D） micron scale computed tomography atlas and a mouse-shaped phantom. Reconstructed results demonstrate the feasibility and effectiveness of the proposed algorithm.     

Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography

In this paper, an efficient l₁-regularized reconstruction method named the primal-dual interior-point (PDIP) method is presented for three-dimensional bioluminescence tomography (BLT) based on the adaptive finite element framework. Taking into account the sparse characteristic of the bioluminescent source, the BLT inverse problem is considered to be a linear programming problem and is represented by its primal and dual form. The source localization and quantification are obtained by solving the primal-dual Newton equation system. The comparisons between PDIP and the classical conjugate gradient least square (CGLS) algorithm are implemented to validate our method. Results from numerical simulation and an in vivo mouse experiment demonstrate the credibility and the potential of the proposed method in practical BLT reconstruction.     

Spectrally resolved bioluminescence optical tomography

Spectrally resolved bioluminescence optical tomography is an approach to recover images of luciferase activity within a volume using multiwavelength emission data from internal bioluminescence sources. The underlying problem of uniqueness associated with nonspectrally resolved intensity-based bioluminescence tomography is highlighted. Reconstructed images of bioluminescence are presented by using as input both simulated and real multiwavelength data from a tissue-simulating phantom. The location of the internal bioluminescence is obtained with 1 mm accuracy. Further, the amplitude of the reconstructed source is proportional to the actual bioluminescence intensity.     

基于CT技术的古琴琴腔构造无损检测研究

古琴的材质特性及制作工艺影响着古琴的品质,同时古琴形制与琴腔布局关系到古琴工艺的完善与传承, 因此在不破坏古琴结构的前提下获取内部琴腔特征与参数十分重要。利用CT无损检测技术对古琴整体进行扫描,得到了琴腔构造断层图,从而研究了古琴面板木纹纹理、面板底板的连接方式和内部缺陷,并运用Mimics软件中的面绘制法实现了古琴琴腔构造的三维重建,使CT断层扫描图像由二维转换为三维立体,更加完整全面地展现古琴琴腔构造形态,最后获得古琴具体琴腔尺寸。实验研究表明,仲尼式与落霞式古琴琴腔构造差异显著,其中仲尼式琴腔表面起伏变化较大,落霞式琴腔表面趋于平缓;仲尼式琴腔体积小于落霞式,琴项位对比明显。通过利用CT无损检测技术实现了对古琴内部信息的准确获取,这对于探究古琴的制作工艺及质量检测起到重要的技术支撑作用,同时也为其他传统珍贵器具内部结构的无损研究提供参考依据。     

数据插值对正电子发射断层成像设备的图像重建影响的研究

正电子发射断层扫描(positron emission computed tomography, PET)是核医学领域最先进的临床检查影像技术. PET技术是目前临床上用于诊断和指导治疗肿瘤的最佳手段之一. 正电子发射断层成像设备探测器采集到的数据需要进行数据处理, 把原始数据转换成正弦图形式的数据才能用于图像重建. 平行束断层重建和扇形束图像重建是图像重建的两种方法, 分别对应平行束和扇形束形式的数据处理方法. 对原始数据的操作不可避免地破坏了原始数据的完整性. 现今, 正电子发射断层设备在重建过程中普遍采用平行束重建的方法. 平行束的数据分离会对PET数据进行插值操作, 扇形束的数据分离不会对PET数据进行插值操作. 本文通过对比平行束图像重建和扇形束图像重建结果, 研究了数据插值对PET图像重建结果的影响. 关键词： 正电子发射计算机断层扫描 数据插值 图像重建 原始数据     

同轴X射线相位衬度计算机X射线断层摄影术研究

基于北京同步辐射装置(BSRF)开展了同轴X射线相位衬度计算机X射线断层摄影术(CT)研究.利用北京同步辐射的14 keV单色X射线作为光源,以高分辨能力的X射线胶片作为探测器,分别开展吸收衬度和同轴相位衬度成像的比较研究以及相位衬度计算机X射线断层摄影术研究.相位衬度计算机X射线断层摄影术重建采用Bronnikov提出的算法.结果显示,与传统的吸收衬度图像相比,相位衬度图像具有更好的衬度和更高的空间分辨力;实验获得人工样品和蝗虫的相位衬度计算机X射线断层摄影术重建图像.重建图像中可见样品的一些结构细节.实验结果表明,相位衬度X射线成像更适合于研究弱吸收或吸收差异很小的材料;利用北京同步辐射开展同轴X射线相位衬度计算机X射线断层摄影术研究是可行的.     

Recent advances in bioluminescence tomography: methodology and system as well as application

Optical molecular imaging has been rapidly developed to noninvasively visualize in vivo physiological and pathological processes involved in normal and suffering organisms at the cellular and molecular levels, in which advanced optical imaging technology and modern molecular biology are being combined to provide a state‐of‐the‐art tool for preclinical biomedical research. Among optical molecular imaging modalities, bioluminescence tomography (BLT) has experienced considerable growth and attracted much attention in recent years for its excellent performance, unique advantages, and high cost‐effectiveness. This article focuses on the genesis and development of BLT, especially for its computational methodology, imaging system, and biomedical application. An overview of the advantages and challenges of the conventional planar bioluminescence imaging technique is first described in comparison with currently available molecular imaging modalities. The imaging algorithms for inverse source reconstruction are classified and summarized according to different a priori knowledge, followed by a simple depiction of the uniqueness theorems of BLT solution. Diverse imaging systems for obtaining three‐dimensional quantitative information of internal bioluminescent sources are then reviewed. The latest application examples of BLT in tumor study and drug discovery are introduced and compared with other mature imaging technologies. Finally, the paper is concluded and an attractive prospect for BLT is predicted.     

Iterative sparse reconstruction of spectral domain OCT signal

We propose and study an iterative sparse reconstruction for Fourier domain optical coherence tomography （FD OCT） image by solving a constrained optimization problem that minimizes L-1 norm. Our method takes the spectral shape of the OCT light source into consideration in the iterative image reconstruction procedure that allows deconvolution of the axial point spread function from the blurred image during reconstruction rather than after reconstruction. By minimizing the L-1 norm, the axial resolution and the signal to noise ratio of image can both be enhanced. The effectiveness of our method is validated using numerical simulation and experiment.     

Standard source method in passive acoustic thermal tomography

Potentialities of passive acoustic thermal tomography in reconstructing the 2D temperature distribution in a human body are studied. Special attention is given to the estimation of the maximal temperature value. A method for its exact reconstruction is proposed. The method uses the assumption that the temperature distribution is formed by a local heat source and is based on the selection of the parameters of such a source by the minimization of the residual of the measured and hypothetical values of the acoustic brightness temperature. The accuracy of the determination of the maximal in-depth temperature by different methods is analyzed by numerical simulation. It is demonstrated that the proposed method provides a higher accuracy than Tikhonov’s methods of global and local regularization, especially with a heat source at great depth. The proposed method is shown to cause no systematic error in the reconstruction of temperature peaks at great depth. The possibility of reconstructing a two-peak temperature distribution by the proposed method is demonstrated.     

Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence

We present a novel fluorescence lifetime tomography system applied to a highly scattering autofluorescent phantom containing live cells expressing the fluorophore enhanced green fluorescent protein (EGFP). The fluorescence signal was excited using a fiber-laser-pumped supercontinuum source and detected using wide-field time gating imaging. To facilitate rapid 3D reconstruction of the fluorescence lifetime distribution, the time-resolved data were Fourier-transformed in time to give complex functions that formed a data set for the Fourier domain reconstruction. Initially the presence of an unspecified background autofluorescence signal impeded reconstruction of the lifetime distribution, but we show that this problem can be addressed using a simple iterative technique.     

利用秩和条件数分析透射式超声CT的数据完备性

为了优化探头设计、估计重构图像误差,提出了一种利用秩和条件数分析透射式超声CT数据完备性的方法。首先分析了透射式超声CT的原理,透射式超声CT的测量方程可以表示成线性方程组,进而透射式超声CT的重构问题可以转化为线性方程组的求解问题。对于所选用的设计方案,描述线性方程组的可解性和解的稳定性的秩和条件数可以用来评估其数据完备性、估计重构图像误差。数学分析和试验结果表明,只有在测量方程组满秩时才可以求得唯一解,在测量误差和介质不均匀性相同时,重构误差近似正比与方程组的条件数,因此可以使用测量方程组的秩和条件数来衡量设计方案的数据完备性,指导实际装置的设计。      

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography (LCT) is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation (TV) minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method (ADM) to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.     

Distinguishing between the interior pressures induced from two independent sources within a room using the probabilistic approach

In this paper, a probabilistic approach is introduced and used to distinguish between the interior pressures that are induced from two independent sound sources within a rectangular room. One source is a vibrating wall of the room and the other is an interior point source. The model is set up using the modal analysis method. In the probabilistic method, the probability densities of the uncertain acoustic model parameters are computed. The values of highest probability density are identified and assigned to the uncertain parameters in the acoustic model. The contributions of the sound sources to the total pressure are then obtained from the acoustic model input with the identified parameters. The effects of the modal truncations, the modeling errors, and the measurement locations on the accuracies of the identification process are studied.     

An inverse spectral analysis of transmission problem in thermo- and photo-acoustic tomography

We study an inverse spectral theory in the thermo- and photo-acoustic tomography in imaging science. Under certain non-trapping hypothesis, we study the zero set of the Fourier transform of the observation data. The zero set corresponds to the spectrum of the interior transmission problem. We reduce the problem into an interior transformation problem of two indices of refractions. The inverse spectral problem is to study the inverse uniqueness of the indices of refraction. The zero distribution theory of entire function plays a role.     

Internal inspection of semi-transparent objects by digital holographic micro-tomography

The combined use of digital holographic microscopy and computer tomography, here named digital holographic micro-tomography, is used to examine the interior of transparent channels. The proposed method is used to identify internal obstacles inside of transparent troughs having slightly different refractive index. The method is based in the acquisition of a set of digital holograms of the specimen whereas it is axially rotated from 0° to 180°. The phase differences retrieved from the obtained holograms are the inputs to a computerised axial tomography procedure. The technique has been numerically modelled in order to find the optimal tomographic conditions and also to realise the minimum difference of refractive index the method could detect. The obtained results show the feasibility of the proposed method for the non-destructive evaluation of transparent micro-objects.     

黄海水体生物发光所致离水辐亮度变化及其与固有光学性质和深度的联系

利用黄海不同季节实测生物发光数据,结合同步测量的固有光学性质数据,基于辐射传输模拟,分析了生物发光所致离水辐亮度（L_w-bio）的数值变化和光谱变化,并讨论其与固有光学性质及生物发光所处深度的联系。主要结论如下：（1）黄海水体L_w-bio幅值不仅具有显著的季节变化特征,同时具有显著的空间变化特征,影响其变化的主要因素除水体本身发光生物的丰度和发光能力外,与水体自身固有光学性质和发光生物所处深度有关。（2）在光谱变化方面,L_w-bio最大峰值波长漂移不仅随着生物发光所处深度加深而增大,同时与固有光学性质有关,在固有光学性质其值较大的水体,当生物发光的光源深度位于表层以下,L_w-bio峰值波长可由蓝光波段（474 nm）变为绿光波段（最大可移动至578 nm）;在固有光学性质其值较小的清澈水体中,辐亮度光谱变化较弱,其L_w-bio峰值波长仍在蓝光波段范围内（最大可移动至500 nm）。（3）黄海海域宽泛的固有光学性质对生物发光光源的几何深度反演影响较大,但可通过L_w-bio的光谱信息,反演光源的几何深度。     

Time reversal and its application to tomography with diffracting sources

An exact time-domain method is proposed to time reverse a transient scalar wave using only the field measured on an arbitrary closed surface enclosing the initial source. Under certain conditions, a time-reversed field can be approximated by retransmitting the measured signals in a reversed temporal order. Exact reconstruction for three-dimensional broadband diffraction tomography (a linearized inverse scattering problem) is proposed by time-reversing the measured field back to the time when each secondary source is excited. The algorithm is verified by a numerical simulation. Extension to the case using Green's function in a heterogeneous medium is discussed.     

求解光学CT图象重建问题的广义脉冲谱技术研究

间接法是目前实现医学诊断用近红外光三维成象(光CT)的最有潜力的手段之一.该方法基于以下假设,即给定分别对应于不同点激励源作用下成象组织体表面各点的传输光测量.在组织体内存在着与上述检测量相对应的、唯一的光学参数三维分布.由此,图象重建变成了特定光子传输模型的逆问题.本文提出采用广义脉冲谱技术(Generalized Pulse Spectrum Technique,GPST)进行光学CT图象重建逆问题的求解.给出了GPST在扩散方程光子传输模型逆问题求解中的具体实现,数值实验结果表明,通过选择合适的复频率点,采用GPST算法的图象重建结果优于其它现有算法,且响应时间合理.最后,本文还初步讨论了吸收和散射系数重建中复频率点选择的一些基本原则。     

Flame four-dimensional deflection tomography with compressed-sensing-revision reconstruction

Deflection tomography with limited angle projections was investigated to visualize a premixed flame. A projection sampling system for deflection tomography was used to obtain chronological deflectogram arrays at six view angles with only a pair of gratings. A new iterative reconstruction algorithm with deflection angle compressed-sensing revision was developed to improve reconstruction-distribution quality from incomplete projection data. Numerical simulation and error analysis provided a good indication of algorithm precision and convergence. In the experiment, 150 fringes were processed, and temperature distributions in 20 cross-sections were reconstructed from projection data in four instants. Four-dimensional flame structures and temperature distributions in the flame interior were visualized using the visualization toolkit. The experimental reconstruction was then compared with the result obtained from computational fluid dynamic analysis.     

Effect of sensor proximity over the non-conformal hologram plane in the near-field acoustical holography based on the inverse boundary element method

Near-field acoustical holography (NAH) is a useful tool for the identification and visualization of vibro-acoustic sources. In particular, NAH can be applied to many practical sources having irregular shape if the inverse boundary element method (BEM) is employed. Once the relation between the source and the radiated field is defined in the transfer matrix modeled by the BEM, the reconstruction of acoustic parameters on the source surface can be conducted by the multiplication of the inverse transfer matrix and the field data measured over the hologram surface. The usual practical way to measure the field data radiated from an irregular shaped source is to adopt a regular hologram surface, which can be a flat, cylindrical, or spherical shape, for the measurement ease. Then, the hologram surface is not conformal to the source surface and the resulting transfer matrix becomes further ill-posed than the conformal case. To investigate the effect of sensor proximity and distance variability on the reconstruction error, simulation and measurement were conducted for an interior problem comprised of a parallelepiped rigid box with a vibrating end plate. Flat, tilted, and randomized hologram surfaces were adopted in the test. It was shown that the reconstruction error is greatly affected by the conditioning of transfer matrix which is related to the positioning of sensor. To improve the reconstruction accuracy, an investigation was conducted to find proper field points among a large number of overdetermined field points. The number of field data was reduced gradually under various reduction schemes using condition number, effective independence value, and sensor distance. It was demonstrated that the quality of reconstruction result given by the non-conformal measurement can be improved by removing some field points that contribute to the ill-conditioning of the inverse problem. A small improvement of the reconstruction accuracy was observed by reducing the field points in the overdetermined situation. However, further reduction of the field points, becoming an underdetermined situation, yielded a drastic improvement of the reconstruction accuracy.