面向近红外脑功能成像的光学自导引漫射光断层成像方法

为降低近红外脑功能漫射光断层成像(DOT)固有的逆问题病态性,并避免多模态方法的图像配准等问题,提出了基于光学自导引提供先验功能信息的脑功能DOT方法(OT-DOT),并发展了图像重构方法.模拟验证表明:上皮厚度(TLT)已知时,OT-DOT获得的重构量化度(QR)约为传统DOT的4.2倍;当TLT的估计误差小于±10%时,OT-DOT重构的QR值可达92%以上,远远优于传统DOT;噪声鲁棒性测试表明,OT-DOT与传统DOT的噪声鲁棒性相近.利用连续光DOT测量系统的仿体实验重构结果表明,所发展的OT-DOT算法获得的重构结果优于传统DOT算法.     

The study of sensitivity and precession of a single-source diffused tomography for detecting of target depth in biological phantom

Optical imaging can be used to study the cancerous stages of breast cancer; and this imaging is noninvasive and safe for healthy tissues. The key problem of optical imaging is the image reconstruction which depends on photon migration in biological tissues; because the study of photon migration in the biological tissues is a complicated problem. The diffusion equation is sometimes used to simulate the photon migration in the biological tissues. Due to limitation of diffusion equation and its approximated nature, we want to explore the accuracy and precision of this method. So in this study, we report the design of a single-source diffuse imaging system with simulating code based on finite element method (FEM) to detect the location of tumor in breast phantoms. The comparison between the reconstructed results and actual values can be considered as a criterion of accuracy of this diffused system. In this experimental setup, to reduce the expense of computational procedure, single source is applied, and the accuracy and precision of this single-source are investigated.     

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.     

An accurate solver for forward and inverse transport

This paper presents a robust and accurate way to solve steady-state linear transport (radiative transfer) equations numerically. Our main objective is to address the inverse transport problem, in which the optical parameters of a domain of interest are reconstructed from measurements performed at the domain’s boundary. This inverse problem has important applications in medical and geophysical imaging, and more generally in any field involving high frequency waves or particles propagating in scattering environments. Stable solutions of the inverse transport problem require that the singularities of the measurement operator, which maps the optical parameters to the available measurements, be captured with sufficient accuracy. This in turn requires that the free propagation of particles be calculated with care, which is a difficult problem on a Cartesian grid.     

一种基于多级小波域分解的时域扩散光学层析成像方法的研究

面向基于有限差分光扩散模型的平板乳腺扩散光学层析反演问题,提出了一种有效提高图像重建质量的方法.与基于全空间域离散像点的传统重建算法不同,本方法采用小波函数对吸收系数和散射系数在空间域进行多尺度分解,在减少低分辨率重建中光学参量的个数、有效改善重建过程病态性的同时,通过逐级细化分解尺度,最终提高了图像的量化度和空间分辨率.数值模拟表明,该方法可实现目标体边对边4 mm的空间分辨率,量化度明显高于传统算法.     

Estimation of optical abnormalities in breast phantom by diffuse equation

Optical imaging is an emerging method for bio-imaging. The advantages of this imaging provide non-ionizing and safe radiation, non-invasive and functional medical imaging. Due to diffusion of photons inside biological tissues, its image processing is complicated. So in spite of these advantages, this imaging method has not been progressed like ultrasound imaging and magnetic resonance imaging (MRI). Also, the penetration depth of photons inside biological phantom is low. To overcome this problem, the complicated diffusion of photons through tissue must be modeled. The diffuse equation can be applied to simulate photons through turbid media like biological tissues. In this paper, the diffuse equation is used to study propagation of diffuse photons. The green function method is applied to solve this equation, and then the optical properties of abnormalities in breast phantom are estimated. This fast method can be applied for image processing.     

基于交替隐式有限差分法的快速早期乳腺癌时域微波断层成像

采用时域微波断层成像技术进行早期乳腺癌检测能够准确地获得乳房的电参数分布,具有明确的物理解释和医学诊断价值.临床应用讲究即时性,为了提高检测的速度,本文将交替隐式有限差分法应用到乳腺癌检测中,基于正反演时间步进成像算法进行成像分析,结果显示在保证精度的前提下,采用交替隐式有限差分法的成像时间可缩短为传统时域有限差分法的23%,提高了微波断层成像技术的临床可应用性.     

Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model

Optical tomography is a novel imaging modality that is employed to reconstruct cross-sectional images of the optical properties of highly scattering media given measurements performed on the surface of the medium. Recent advances in this field have mainly been driven by biomedical applications in which near-infrared light is used for transillumination and reflectance measurements of highly scattering biological tissues. Many of the reconstruction algorithms currently utilized for optical tomography make use of model-based iterative image reconstruction (MOBIIR) schemes. The imaging problem is formulated as an optimization problem, in which an objective function is minimized. In the simplest case the objective function is a normalized-squared error between measured and predicted data. The predicted data are obtained by using a forward model that describes light propagation in the scattering medium given a certain distribution of optical properties.In part I of this two-part study, we presented a forward model that is based on the time-independent equation of radiative transfer. Using experimental data we showed that this transport-theory-based forward model can accurately predict light propagation in highly scattering media that contain void-like inclusions. In part II we focus on the details of our image reconstruction scheme (inverse model). A crucial component of this scheme involves the efficient and accurate determination of the gradient of the objective function with respect to all optical properties. This calculation is performed using an adjoint differentiation algorithm that allows for fast calculation of this gradient. Having calculated this gradient, we minimize the objective function with a gradient-based optimization method, which results in the reconstruction of the spatial distribution of scattering and absorption coefficients inside the medium. In addition to presenting the mathematical and numerical background of our code, we present reconstruction results based on experimentally obtained data from highly scattering media that contain void-like regions. These types of media play an important role in optical tomographic imaging of the human brain and joints.     

超宽带微波检测早期乳腺肿瘤三维仿真

超宽带微波成像技术可作为有效的方法用于乳房早期乳腺肿瘤的检测. 该方法基于乳房组织和肿瘤之间较大的电学特性差异的特点进行成像, 能提供足够的分辨率以及足够的穿透深度. 本文采用时域有限差分方法建立超宽带微波信号在三维乳房组织中传播的模型, 并采用单极德拜模型完成了生物组织色散特性的模拟. 利用8发9收的天线阵列实现微波肿瘤探测, 利用共焦成像算法对乳房组织进行图像重构并进行肿瘤定位. 仿真结果显示共焦成像算法能够实现最小直径3 mm的肿瘤的检测, 同时证实了超宽带微波成像技术应用于早期乳腺肿瘤检测的有效性. 关键词： 微波成像 肿瘤检测 时域有限差分 共焦成像算法     

Diffuse optical tomography: Present status and its future

Diffuse optical tomography (DOT) is one of the emerging modalities for the non-invasive imaging of thick biological tissues using near-infrared (NIR) light. This article reviews the fundamentals and development of DOT technology since its advent in the early 1990s, including the modeling of light propagation in biological tissues which strongly scatter and weakly absorb NIR light, the optical properties of biological tissues in the NIR wavelength range, three typical measurement methods, image reconstruction algorithms, and so forth. Then various studies are referred to for improvement of the DOT images, which are essentially low in quality due to the ill-conditioned and underdetermined problem. Studies and clinical applications presently attracting much attention are discussed in some detail. Finally, the expected future developments are summarized.     

Convergence rate calculation of simultaneous iterative reconstruction technique algorithm for diffuse optical tomography image reconstruction: A feasibility study

Diffuse optical tomography (DOT) is an emerging technique for functional biological imaging. The imaging quality of DOT depends on the imaging reconstruction algorithm. The SIRT has been widely used for DOT image reconstruction but there is no criterion to truncate based on any kind of residual parameter. The iteration loops will always be decided by experimental rule. This work presents the CR calculation that can be great help for SIRT optimization. In this paper, four inhomogeneities with various shapes of absorption distributions are simulated as imaging targets. The images are reconstructed and analyzed based on the simultaneous iterative reconstruction technique (SIRT) method. For optimization between time consumption and imaging accuracy in reconstruction process, the numbers of iteration loop needed to be optimized with a criterion in algorithm, that is, the root mean square error (RMSE) should be minimized in limited iterations. For clinical applications of DOT, the RMSE cannot be obtained because the measured targets are unknown. Thus, the correlations between the RMSE and the convergence rate (CR) in SIRT algorithm are analyzed in this paper. From the simulation results, the parameter CR reveals the related RMSE value of reconstructed images. The CR calculation offers an optimized criterion of iteration process in SIRT algorithm for DOT imaging. Based on the result, the SIRT can be modified with CR calculation for self-optimization. CR reveals an indicator of SIRT image reconstruction in clinical DOT measurement. Based on the comparison result between RMSE and CR, a threshold value of CR (CR_T) can offer an optimized number of iteration steps for DOT image reconstruction. This paper shows the feasibility study by utilizing CR criterion for SIRT in simulation and the clinical application of DOT measurement relies on further investigation.     

Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization

As a part of resolving optical properties in atmosphere radiative transfer calculations, this paper focuses on obtaining aerosol optical thicknesses (AOTs) in the visible and near infrared wave band through indirect method by gleaning the values of aerosol particle size distribution parameters. Although various inverse techniques have been applied to obtain values for these parameters, we choose a stochastic particle swarm optimization (SPSO) algorithm to perform an inverse calculation. Computational performances of different inverse methods are investigated and the influence of swarm size on the inverse problem of computation particles is examined. Next, computational efficiencies of various particle size distributions and the influences of the measured errors on computational accuracy are compared. Finally, we recover particle size distributions for atmospheric aerosols over Beijing using the measured AOT data (at wavelengths λ=0.400, 0.690, 0.870, and 1.020 μm) obtained from AERONET at different times and then calculate other AOT values for this band based on the inverse results. With calculations agreeing with measured data, the SPSO algorithm shows good practicability.     

Analytical one-dimensional model for laser-induced ultrasound in planar optically absorbing layer

Ultrasound generated by means of laser-based photoacoustic principles are in common use today and applications can be found both in biomedical diagnostics, non-destructive testing and materials characterisation. For certain measurement applications it could be beneficial to shape the generated ultrasound regarding spectral properties and temporal profile. To address this, we studied the generation and propagation of laser-induced ultrasound in a planar, layered structure. We derived an analytical expression for the induced pressure wave, including different physical and optical properties of each layer. A Laplace transform approach was employed in analytically solving the resulting set of photoacoustic wave equations. The results correspond to simulations and were compared to experimental results. To enable the comparison between recorded voltage from the experiments and the calculated pressure we employed a system identification procedure based on physical properties of the ultrasonic transducer to convert the calculated acoustic pressure to voltages. We found reasonable agreement between experimentally obtained voltages and the voltages determined from the calculated acoustic pressure, for the samples studied. The system identification procedure was found to be unstable, however, possibly from violations of material isotropy assumptions by film adhesives and coatings in the experiment. The presented analytical model can serve as a basis when addressing the inverse problem of shaping an acoustic pulse from absorption of a laser pulse in a planar layered structure of elastic materials.     

Multi-bright-dark soliton solutions to the AB system in nonlinear optics

The AB system is the basic integrable model to describe unstable baroclinic wave packets in geophysical fluids and the propagation of mesoscale gravity flows in nonlinear optics. On the basis of the spectral analysis of a Lax pair and the inverse scattering method, we establish the Riemann–Hilbert problem of the AB system. Then, the inverse problems are formulated and solved with the aid of the Riemann–Hilbert problem, from which the potentials can be reconstructed according to the asymptotic expansion of the sectional analytic function and the related symmetry relations. As an application, we obtain the multi-bright-dark soliton solutions to the AB system in the reflectionless case and discuss the dynamic behavior of elastic soliton collisions by choosing appropriate free parameters.     

Improving depth resolution of diffuse optical tomography with an exponential adjustment method based on maximum singular value of layered sensitivity

The sensitivity of diffuse optical tomography (DOT) imaging exponentially decreases with the increase of photon penetration depth, which leads to a poor depth resolution for DOT. In this letter, an exponential adjustment method (EAM) based on maximum singular value of layered sensitivity is proposed. Optimal depth resolution can be achieved by compensating the reduced sensitivity in the deep medium. Simulations are performed using a semi-infinite model and the simulation results show that the EAM method can substantially improve the depth resolution of deeply embedded objects in the medium. Consequently, the image quality and the reconstruction accuracy for these objects have been largely improved.     

Local diffusion regularization method for optical tomography reconstruction by using robust statistics

We formulate a solution to the diffuse optical tomography (DOT) inverse problem as the minimization of an energy functional of the solution and the data. For the solution prior we introduce a local diffusion regularization potential with a threshold based on robust statistics (the Hubert function). We compare results on simulated data for the Hubert function and two other standard regularization functionals, Tikhonov and total variation.     

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     

Geometrical interpretation of acoustic holography: Adaptation of the propagator and minimum quality guaranteed in the presence of errors

A large number of inverse problems in acoustics consist of a reverse propagation of the acoustic pressure measured with an array of microphones. The goal is usually to identify the acoustic source location and strength or the surface velocity of a vibrating structure. The quality of the results obtained depends on the propagation model, on the accuracy of the pressure measurements and, finally, on the inverse problem conditioning. How to quantify this quality is the issue addressed in this paper. For this purpose, a geometrical interpretation of the inverse acoustic problem is proposed. The main application will, eventually, be near-field acoustic holography (NAH), but it is expected that the proposed approach will also apply to other types of inverse acoustic problems. First, the geometrical representation of the inverse problem is proposed. The inverse problem is stated from a direct linear problem in the frequency domain. For each frequency, an overdetermined system of linear complex algebraic equations must be inverted. The concept of quality is discussed and a quality index is proposed based upon the residue of the inverse problem, solved in a mean square sense. Then, a simple one-dimensional (plane wave) acoustic example consisting of a source and two pressure measurements is used to illustrate the proposed geometrical representation of the inverse problem and the quality criterion inspired by it. In the simple example, the propagation model can be improved by searching for a reflection coefficient at the origin of the simulated hologram. This reflection coefficient is used to simulate the presence of a hidden source placed behind the source. An artificial attenuation is introduced to simulate the effect of geometrical attenuation present in real NAH problems. Again, using the geometrical representation, it is shown how, from an improved propagation model together with a given measurement noise level in the hologram, one can guarantee a certain quality level of the inverse procedure. Finally, numerical results show, in a preliminary way, how the identified source strength converges towards the exact velocity when the estimated propagation model tends to the exact propagation model.     

Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures

We discuss numerical algorithms for the determination of periodic surface structures from light diffraction patterns. With decreasing details of lithography masks, increasing demands on metrology techniques arise. Scatterometry as a non-imaging indirect optical method is applied to simple periodic line structures in order to determine parameters like side-wall angles, heights, top and bottom widths and to evaluate the quality of the manufacturing process. The numerical simulation of diffraction is based on the finite element solution of the Helmholtz equation. The inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns. Restricting the class of gratings and the set of measurements, this inverse problem can be reformulated as a non-linear operator equation in Euclidean spaces. The operator maps the grating parameters to special efficiencies of diffracted plane-wave modes. We employ a Gauß –Newton type iterative method to solve this operator equation. The reconstruction properties and the convergence of the algorithm, however, is controlled by the local conditioning of the non-linear mapping. To improve reconstruction and convergence, we determine optimal sets of efficiencies optimizing the condition numbers of the corresponding Jacobians. Numerical examples for chrome-glass masks and for inspecting light of wavelength 632.8 nm are presented.     

离体正常乳腺组织350～850 nm波段光谱特性

采用带有积分球附件的紫外/可见/近红外分光光度计测量了离体正常乳腺组织在350～850 nm光谱范围的反射率和透射率,运用反向倍加法得到了离体正常乳腺组织在相应光谱范围的光学参数,分析了正常乳腺组织的光学穿透深度随波长的变化情况。实验结果表明：350～850 nm波段正常乳腺组织的约化散射系数μ′_s大于吸收系数μ_a。μ′_s随着波长的增加而减小,即从350 nm波长值为9.731 mm-1～850 nm波长值为1.476 mm-1。μ_a从350 nm波长值为0.798 mm-1～850 nm波长值为0.102 mm-1,410 nm波长处存在一个吸收峰,其值为0.506 mm-1。光学穿透深度随着波长的增加而增大,从350 nm波长值为0.199 mm-1～850 nm波长值为1.439 mm。基于反向倍加法计算获得乳腺组织的光学参数,采用Monte Carlo模拟得到其相应光谱范围的反射率和透射率,并与实际测量值进行比较,二者的一致性较好。实验结果为乳腺组织的光活检及其光学治疗提供重要参考。