A multi-phase level set framework for source reconstruction in bioluminescence tomography

We propose a novel multi-phase level set algorithm for solving the inverse problem of bioluminescence tomography. The distribution of unknown interior source is considered as piecewise constant and represented by using multiple level set functions. The localization of interior bioluminescence source is implemented by tracing the evolution of level set function. An alternate search scheme is incorporated to ensure the global optimal of reconstruction. Both numerical and physical experiments are performed to evaluate the developed level set reconstruction method. Reconstruction results show that the proposed method can stably resolve the interior source of bioluminescence tomography.     

一种光学层析图像的多准则重建方法

光学层析成像是一个病态重建问题,为克服重建过程的病态性,提出将多准则优化理论引入到图像重建中。利用了三个用于光学层析图像重建的准则:平方误差函数、图像熵函数和局部平滑函数。采用向量优化方法将多准则优化问题转化为单准则优化问题求解。为了确定各个目标函数间的权重系数,提出一种动态权重系数求解方法。重建过程目标函数关于光学参量的梯度计算是关键,因此提出一种基于梯度树的计算方法。实验过程中对多准则重建结果和基于平方误差函数的单准则重建结果做了比较,证明该方法能够克服传统的偏重单一目标的单准则重建的不足,有效地重建光学层析图像,提高图像重建质量。     

Comparison of the efficiencies of Fourier and wavelet expansions in passive acoustic thermal tomography

A comparison of the accuracy achieved in temperature-distribution reconstruction by the Fourier and wavelet expansions in passive acoustic tomography is carried out. Since the use of focused ultrasound in hyperthermia leads to local heating of the tissue, the wavelet representation of such temperature distributions with local fluctuations is more compact than their Fourier representation. It is demonstrated that the compactness of the wavelet representation provides an opportunity to reduce considerably the number of unknown quantities in solving the inverse problem of acoustic thermal tomography and to increase the accuracy of the temperature-distribution reconstruction in comparison with the case of using the Fourier representation. A method for choosing a compact wavelet basis for temperature distributions obtained in the hyperthermia process is proposed.     

TOMOGRAPHY FORMULA FOR BIOCHEMICAL IMAGING OF THIN TISSUE WITH DIFFUSE-PHOTON DENSITY WAVES

Using the transport theory to describe the near infrared light propagating in tissue with finite parallel-plane geometry, and taking the zero-boundary condition, we obtain the analytical expression of average photon density and Green's function incorporating the boundary effects in the homogeneous tissure. Making use of perturbation theory we also obtain the analytical expression of scattered wave induced by the heterogeneity, and present the 2-dimensional spatial transform of scattered wave with respect to transverse coordinate. If the information of heterogeneity on depth and thickness is available, diffraction tomography formula is presented to save the time of image reconstruction; if the information is unknown, we suggest to obtain the inhomogeneous function from the one-dimensional integral equation of 2-dimensional spatial transform of scattered wave applying the direct matrix method or iterative method for image reconstruction. This approach avoids directly solving three-dimensional integral equation of scattered wave. In our proposed approach the strong points of the direct matrix method, iterative method, and diffraction tomography are fully combined.     

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.     

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.     

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.     

An Acceleration Algorithm for Image Reconstruction Based on Continuous-Discrete Mapping Model

In image reconstruction for X-ray computed tomography, images reconstructed by filtered backprojection (FBP) include systematic errors because the FBP method does not take into account some of the properties of the actual imaging system such as the divergence of X-ray beam. One solution to this problem is to use algebraic reconstruction methods, such as generalized analytic reconstruction from discrete samples and natural pixel decomposition. However, in the process of reconstruction using these methods, it is necessary to solve the linear algebraic equations which have a large coefficient matrix. In this paper, we propose a method to accelerate the iteration solving these equations by preconditioning the coefficient matrix using a polynomial function. The results of the computer simulations show the effectiveness of the proposed method.     

Optical tomography with the discontinuous Galerkin formulation of the radiative transfer equation in frequency domain

Optical tomography is an inverse method of probing semi-transparent media with the help of light sources. The reconstruction of the optical properties usually employs finite volumes or continuous finite elements formulations of light transport as a forward model for the predictions. In a previous study, we have introduced a generalization of the inversion approach with finite elements formulations by using an integral form of the objective function. The novelty is that the surfaces of the detectors are taken into account in the reconstruction and compatibility is obtained for all finite element formulations. This present paper illustrates this new approach by developing a Discontinuous Galerkin formulation as a forward model for an optical tomography application in the frequency domain framework. Numerical tests are performed to gauge the accuracy of the method in recovering optical properties distribution with a gradient-based algorithm where the adjoint method is used to fastly compute the objective function gradient. It is seen that the reconstruction is accurate and can be affected by noise on the measurements as expected. Filtering of the gradient at each iteration of the reconstruction is used to cope with the ill-posed nature of the inverse problem and to improves the quality and accuracy of the reconstruction.     

Compressive sampling photoacoustic tomography based on edge expander codes and TV regularization

A new photoacoustic （PA） signal sampling and image reconstruction method, called compressive sampling PA tomography （CSPAT）, is recently proposed to make low sampling rate and high-resolution PA tomogra- phy possible. A key problem within the CSPAT framework is the design of optic masks. We propose to use edge expander codes-based masks instead of the conventional random distribution masks, and efficient total variation （TV） regularization-based model to formulate the associated problem. The edge expander codesbased masks, corresponding to non-uniform sampling schemes, are validated by both theoretical analysis and results from computer simulations. The proposed method is expected to enhance the capability of CSPAT for reducing the number of measurements and fast data acquisition.     

Few-Projection Tomography. II. Radioastronomical Method CLEAN for Three-Dimensional Problems

The radioastronomical method CLEAN is extended to problems of three-dimensional (3D) tomographic reconstruction. We consider two options, namely, 3D_1D (reconstruction using one-dimensional projections) and 3D_2D (reconstruction based on using two-dimensional projections). Deconvolution with the use of the synthesized beam (equivalent total transfer function) makes it possible to reduce several times the number of aspects in comparison with the conventional approach. We point out the relationship between the maximum level of sidelobes of the synthesized ray constructed for the Gaussian transfer functions and the number of used projections. In the case of 3D_2D -reconstruction, the reconstruction quality similar to that for the 2D_1D case is only achieved if the same number of uniformly distributed projections are used in both cases. The use of one-dimensional projections for the 3D_1D -reconstruction requires doubling of the number of projections. The reconstruction process is illustrated by an example of the three-dimensional model of an optically thin radiating object. We consider the possibilities of using the developed approach in astrotomography and remote sensing based on introducing the transfer functions which determine resolution of the receiving beam patterns and spectrographs, as well as temporal resolution of the sensing profiles. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 367–381, May 2005.     

Levenberg–Marquardt iterative regularization for the pulse-type impact-force reconstruction

In this paper, we study the Levenberg–Marquardt algorithm with the trust region strategy to iteratively solve the ill-posed impact-force reconstruction problem. This particular problem is interesting because the impact-force particularly those of the pulse-type are difficult to be measured directly. In the present approach, the necessity of regularization is enforced by means of the trust region approach. This study mainly contributes a systematic approach to locate the optimal solution by tracking the Levenberg–Marquardt parameter. The proposed method is evaluated by solving two typical problem existed in the inverse problem of the impact-force reconstruction. Reasonable accurate impact-forces were produced from the both evaluations.     

基于约束优化的闪光照相图像重建算法

针对闪光照相图像受模糊及噪声影响的问题,提出了一种基于约束优化的闪光照相图像重建算法。该算法建立基于平行束投影的正向成像矩阵,并通过嵌入模糊矩阵表达成像过程中的模糊因素,采用最速下降法求解重建问题。在算法中设计了预优矩阵以提高迭代重建速度,利用客体密度值非负、密度分布分段光滑并含有阶跃性边界的先验知识,设计和采用了非负约束、光滑约束及广义变分边界约束条件。对仿真FTO客体图像及实际闪光照相图像的重建结果表明,基于约束优化的重建算法具有良好的边界保持能力及噪声抑制能力,可以有效提高图像重建质量。     

A new inverse approach for the equivalent gray radiative property of a non-gray medium using a modified zonal method and the complex-variable-differentiation method

Non-gray radiative properties of an absorbing, emitting, non-gray participating medium significantly increase the difficulty of solving the radiative transfer equation. This paper presents a new inverse approach for the equivalent gray radiative property of a non-gray medium. In this approach, the unknown equivalent gray radiative properties are treated as the optimization variables, and the errors to be minimized are the differences between the calculated temperatures and the measured ones. The measured data are simulated by solving the direct problem, in which a modified zonal method together with the Edwards exponential wide-band model is employed. In the inverse problem, the sensitivity coefficients are first calculated by the complex-variable-differentiation method, and then the least-square method and the Newton-Raphson iterative method are employed to minimize the target function. The effectiveness and efficiency of the inverse problem are demonstrated in an example, and another case is given to show the accuracy and potential of the proposed algorithm. The effects of the measurement error and the number of measurement points on the accuracy of the inverse analysis are also investigated in detail.     

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.     

An Efficient Computational Algorithm for Implementing the Maximum Entropy Method in Deconvolution Inversion Problems

We discuss a theoretical informational approach to solving ill-posed problems of function recovery based on the use of the maximum entropy principle. On this basis, we propose an efficient computational algorithm for implementing the procedure of solving the function-recovery problem and the method of regularization of the problem of function recovery from the convolution. In many cases, the proposed regularization method ensures high recovery quality. If the recovery accuracy is insufficient, then the Largange multipliers obtained by this method can be the best initial approximation (in the sense of the least squares) for their iterative refinement.     

不确定动态混沌系统的最优控制

对于混沌系统的控制问题,考虑到控制系统能量限制的要求,首先确立一个二次目标函数,然后给出了求解最优控制律的一个简单方法,该方法通过求解线性二次最优控制问题,获得了混沌系统的最优控制律,避免了求解非线性Hamilton-Jacobi-Bellman 偏微分方程(HJB方程)的困难.利用Lyapunov方法证明了闭环系统的稳定性.对统一混沌系统和Liu混沌系统的仿真结果表明了控制策略的有效性.     

Fast reconstruction in fluorescence molecular tomography using data compression of intra- and inter-projections

In order to improve the reconstruction accuracy in fluorescence molecular tomography(FMT), a common approach is to increase the number of fluorescence data or projections. However, this approach consumes too much memory space and computational time. In this Letter, a data compression strategy that involves the removal of the redundant information from both intra- and inter-projections is proposed to reduce the dimension of the FMT inverse problem. The performance of this strategy is tested with phantom and in vivo mouse experiments.The results demonstrate that the proposed data compression strategy can accelerate the FMT reconstruction nearly tenfold and almost without any quality degradation.     

不确定动态混沌系统的最优控制

对于混沌系统的控制问题,考虑到控制系统能量限制的要求,首先确立一个二次目标函数,然后给出了求解最优控制律的一个简单方法,该方法通过求解线性二次最优控制问题,获得了混沌系统的最优控制律,避免了求解非线性Hamilton-Jacobi-Bellman偏微分方程(HJB方程)的困难.利用Lyapunov方法证明了闭环系统的稳定性.对统一混沌系统和Liu混沌系统的仿真结果表明了控制策略的有效性.