In-vivo fluorescence molecular tomography based on optimal small animal surface reconstruction

Accurate small animal surface reconstruction is important for full angle non-contact fluorescence molecular tomography （FMT） systems. In this letter, an optimal surface reconstruction method for FMT is proposed. The proposed method uses a line search method to minimize the mismatch between the reconstructed three- dimensional （3D） surface and the projected object silhouette at different angles. The results show that the mean mismatches of the 3D surfaces generated on three live anesthetized mice are all less than two charge coupled device （CCD） pixels （0.154 mm）. With the accurately reconstructed 3D surface, in-vivo FMT is also performed.     

Estimation of Electrical Source Localization Using the Temporal Correlation between Magnetic Field Measurements

It is well known that an inverse problem of biomagnetic imaging is generally ill-posed. Recently several attempts using biocoherence have been reported, but the ill-condition is not considered in these previous methods. If the conventional reconstruction formula is under the ill-condition, the reconstruction problem is also ill-posed and the ill-posedness cannot be improved. In this paper, we propose an approach to estimate the location of current sources under the condition that sources of different positions have little or weak correlation. Our method is based on a well-known regularization method, the truncated SVD method. Compared with the conventional method, our technique allows accurate determination of the location of current sources because it improves the ill-posedness of the inverse problem. We carried out computer simulations using the half-space conducting model and confirmed the effectiveness of our method.     

Tikhonov-regularization-based projecting sparsity pursuit method for fluorescence molecular tomography reconstruction

For fluorescence molecular tomography(FMT),image quality could be improved by incorporating a sparsity constraint.The L1 norm regularization method has been proven better than the L2 norm,like Tikhonov regularization.However,the Tikhonov method was found capable of achieving a similar quality at a high iteration cost by adopting a zeroing strategy.By studying the reason,a Tikhonov-regularization-based projecting sparsity pursuit method was proposed that reduces the iterations significantly and achieves good image quality.It was proved in phantom experiments through time-domain FMT that the method could obtain higher accuracy and less oversparsity and is more applicable for heterogeneous-target reconstruction,compared with several regularization methods implemented in this Letter.     

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.     

Revisiting the normalized Born approximation: effects of scattering

The normalized Born approximation has been suggested as a ratiometric method in fluorescence molecular tomography (FMT) applications, to account for heterogeneity variations. The method enabled practical inversions, as it offered fluorescence reconstruction accuracy over a wide range of absorption heterogeneity, while also accounting for unknown experimental factors, such as the various system gains and losses. Yet it was noted that scattering variations affect the robustness and accuracy. Herein we decompose the effects of absorption and scattering and capitalize on the recent development of hybrid FMT/x-ray computed tomography imaging methods to proposed amendments to the method, which improve the overall accuracy of the approach.     

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.     

快速估计荧光分子断层成像中单个荧光物的深度

荧光分子断层成像支持在体无创研究长时间跨度的分子事件,满足21世纪系统化地观测生命过程的要求。在其复杂且耗时的重建中,先验信息有助于加快重建速度,提高重建图像的质量。文章将求解荧光物的深度作为待优化问题,由单幅荧光图像直接快速地估计深度信息。首先根据生物组织内的扩散模型和外推边界条件,推导出生物体边界上两点处荧光强度的比值R_f。然后用粒子群优化算法,在吸收系数和散射系数的估计区间内,由最小化生物体边界上两点处模型值RM_f与测量值RT_f之间的差,估计出荧光物的深度。不同尺寸荧光物的两个仿体实验的结果表明,所提出的方法不需要网格剖分和重建,能快速简单地估计出单个类似于球体的荧光物的深度。     

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.     

Review of force reconstruction techniques

An important engineering problem is the recovery of the input of a system given its output. This is a difficult problem to solve in that it is often an ill-defined problem. Such ill-posedness is problematic since noise becomes very influential and results in inaccurate or non-unique solutions. To combat this ill-posedness, additional constraints are typically applied to redefine the problem, leading to a well-defined problem with a unique solution. Current input reconstruction methods span the spectrum of analysis and computation, and we have grouped them into three categories: Direct, Regularization, and Probabilistic/Statistical. Each of these groups is divided into several subsets that offer different perspectives in which to view the reconstruction problem. Our primary interests lie in the behavior of mechanical systems and, as such, we have focused on the literature in these fields. However, applicability includes other fields with the same and similar governing equations.     

On optimal retreat distance for the equivalent source method-based nearfield acoustical holography

As a basic form of the equivalent source method (ESM) that is used to nearfield acoustical holography (NAH) problems, discrete monopoles are utilized to represent the sound field of interest. When setting up the virtual source distribution, it is vital to maintain a "retreat distance" between the virtual sources and the actual source surface such that reconstruction would not suffer from singularity problems. However, one cannot increase the distance without bound because of the ill-posedness inherent in the reconstruction process with large distance. In prior research, 1-2 times lattice spacing, or the inter-element distance of microphones, is generally recommended as retreat distance in using the ESM-based NAH. While this rule has shown to yield good results in many cases, the optimal choice is a complicated issue that depends on frequency, geometry of the physical source, content of evanescent waves, distribution of sensors and virtual sources, etc. This paper deals about attaining the best compromise between the reconstruction errors induced by the point source singularity; the reconstruction ill-posedness is an interesting problem in its own right. The paper revisits this issue, with the aid of an optimization algorithm based on the golden section search and parabolic interpolation. Numerical simulations were conducted for a baffled planar piston source and a spherically baffled piston source. The results revealed that the retreat distance appropriate for the ESM ranged from 0.4 to 0.5 times the spacing for the planar piston, while from 0.8 to 1.7 times average spacing for the spherical piston. Experiments carried out for a vibrating aluminum plate also revealed that the retreat distance with 0.5 times the spacing yielded better reconstructed velocity than those with 1/20 and 1 times the spacing.     

时域荧光分子层析图像重建的线性特征数据法

通过扩展用于时域扩散光成像(Diffuse Optical Tomography, DOT)的广义脉冲谱技术,提出了一种用于时域荧光分子层析成像(Fluorescence Molecular Tomography, FMT)的线性特征数据图像重建算法.此算法能够同时重建荧光产率和荧光寿命,并且利用模拟数据对此方法进行验证,证明了算法的有效性.     

联合波叠加法的全息理论与实验研究

当空间声场中同时存在多个相干声源时，运用常规近场声全息方法无法重建每个相干声源表面的声学信息，当然也无法预测每个声源单独产生的空间声场，相干声场的全息重建与预测已成为全息技术推广应用过程中亟待解决的问题.在提出联合波叠加法并将其应用于空间声场变换的基础上，对其进行了实验研究.通过对实际相干声场的全息重建与预测，验证了常规波叠加法在相干声场重建中的局限性、联合波叠加法在相干声场全息重建与预测过程的可行性和准确性，还研究了Tikhonov正则化方法在抑制声学逆问题的非适定性中的有效性和滤波系数的选择原则的可行性，以提高全息重建与预测的精度. 关键词： 近场声全息 联合波叠加 相干声场 Tikhonov正则化     

AN INVERSE AEROACOUSTIC PROBLEM ON ROTOR WAKE/STATOR INTERACTION

An inverse aeroacoustic model on rotor wake/stator interaction is proposed based on the linearized Euler equations. The sound field is related to the pressure distribution on the stator surface in the form of a Fredholm integral equation of the first kind which is a well-known ill-posed problem. Since the sound field is fully specified, numerical inversion allows the reconstruction of the pressure distribution on the stator surface. For solving the discrete ill-posed problem, the singular-value decomposition technique coupled with the Tikhonov regularization method is applied to stabilize the solution. The optimal regularization parameter is chosen by the generalized cross-validation criterion and the discrete Picard condition is employed to analyze the ill-posedness of the inverse problem. Numerical results show that the reconstruction is fairly good when the signal-to-noise ratio is not very low. The results become inaccurate when the noise dominates over the observer signal. In addition, numerical results also indicate the importance of the reduced frequency. The higher the reduced frequency, the better the reconstruction results.     

二维有耗色散介质的时域逆散射方法

为了重建二维有耗色散介质的电参数分布,基于Debye模型,应用泛函分析和变分法,提出一种时域逆散射新方法.该方法首先以最小二乘准则构造目标函数,将逆问题表示为约束最小化问题,接着应用罚函数法转化为无约束最小化问题,然后基于变分计算导出闭式的Lagrange函数关于特征参数的Fréchet导数,最后借助梯度算法和时域有限差分法迭代反演Debye模型参数.为了对抗噪声污染和逆问题的病态特性,采用了一阶Tikhonov正则化方法.数值应用中,利用Polak-Ribière-Polyak非线性共轭梯度法,对二维乳     

傅里叶-梅林变换(FMT)在畸变-不变图像识别中的应用

针对尺度缩放和角度旋转变化目标相关识别率低的问题,在联合相关识别中加入傅里叶-梅林变换方法.采用傅里叶-梅林变换(FMT)中的对数极坐标变换、梅林变换、傅里叶变换具有的旋转、尺度、平移(RST)不变性,可以提高JTC图像识别的性能,实现畸变-不变图像的识别.利用联合变换相关器对角度旋转0°～40°、尺度变化0～20%的目标进行计算机仿真实验.实验结果表明:在JTC中采用FMT可以实现畸变-不变图像的识别.     

Recovering doping profiles in semiconductor devices with the Boltzmann–Poisson model

We investigate numerically an inverse problem related to the Boltzmann–Poisson system of equations for transport of electrons in semiconductor devices. The objective of the (ill-posed) inverse problem is to recover the doping profile of a device, presented as a source function in the mathematical model, from its current–voltage characteristics. To reduce the degree of ill-posedness of the inverse problem, we proposed to parameterize the unknown doping profile function to limit the number of unknowns in the inverse problem. We showed by numerical examples that the reconstruction of a few low moments of the doping profile is possible when relatively accurate time-dependent or time-independent measurements are available, even though the later reconstruction is less accurate than the former. We also compare reconstructions from the Boltzmann–Poisson (BP) model to those from the classical drift–diffusion-Poisson (DDP) model, assuming that measurements are generated with the BP model. We show that the two type of reconstructions can be significantly different in regimes where drift–diffusion-Poisson equation fails to model the physics accurately. However, when noise presented in measured data is high, no difference in the reconstructions can be observed.     

Spectrofluorimetric Determination of Famotidine in Pharmaceutical Preparations and Biological Fluids. Application to Stability Studies

A simple, economic, selective, and stability indicating spectrofluorimetric method was developed for the determination of famotidine (FMT); is based on its reaction with 9, 10-phenanthraquinone in alkaline medium to give a highly fluorescent derivative measured at 560 nm after excitation at 283 nm. The fluorescence intensity - concentration plot was rectilinear over the concentration range of 50–600 ng/ml with minimum quantification limit (LOQ) of 13.0 ng/ml and minimum detection limit (LOD) of 4.3 ng/ml. The factors affecting the development of the fluorescence intensity of the reaction product were carefully studied and optimized. The method was applied for the determination of FMT in its dosage forms. The stability of the compound was studied, and the proposed method was found to be stability indicating one. The results obtained were in good agreement with those obtained by the official method. Furthermore, the method was applied for the determination of FMT in spiked and real human plasma. The mean % recovery (n = 4) was found to be 99.94 ± 0.24, and 105.13 ± 0.64 for spiked and real human plasma, respectively. The composition of the reaction product as well as its stability constant was also investigated. Moreover, the method was utilized to investigate the kinetics of both alkaline and oxidative induced degradation of the drug. The apparent first order rate constant and half life time of the degradation product was calculated. A proposal of the reaction pathway was postulated.     

基于逆散射理论的地震波速度正则化反演

本文基于逆散射理论利用正则化有限差分对比源反演算法对地震波传播速度进行反演, 该方法是基于波动方程的频率域波形反演算法, 利用非线性共轭梯度法, 通过最小化目标优化函数不断迭代更新速度模型. 由于地球物理反演问题的病态性和不稳定性, 通过基于反演参数总变差的正则化处理, 使反演问题变为良性问题且算法具有较强的抗噪声干扰能力. 反演过程中使用了频率-空间域9点差分正演算子以及PML吸收边界条件. 与其他反演算法相比, 由于背景模型在反演迭代过程中保持不变, 可以避免在每次迭代过程中重新构造正演算子及矩阵分解等相关计算过程, 使得该算法非常适合于大规模三维反演计算. 此外, 本文采用基于MPI的并行计算, 进一步提高了反演计算的效率. 二维CSEG模型反演结果表明该方法可以反演得到高分辨率的地震波速度重建结果, 为地震勘探数据处理及解释提供准确的速度信息.     

多级轴流压气机内部流场诊断问题的数值解法

多级轴流压气机内部流场诊断问题的数值解法张增产（清华大学力学系北京１０００８４）刘杰,叶大均（清华大学热能工程系北京１０００８４）关键词流场诊断;压气机１引言压气机是航空发动机中的核心部件。但是压气机的研制是一项既复杂又困难的工作,必须进行大量的实验...     

Studies on adsorption energy distributions computation from adsorption isotherms by the ansatz method

Since the well-known adsorption integral equation (AIE) is an ill-posed problem, calculation of relevant energetic properties from gas and liquid adsorption isotherms on porous solids still remains a challenging field of research. There are two approaches for solving the AIE: (1) the numerical regularization method and (2) the fitting of the experimental adsorption data by functions possessing an analytical solution. Up to now the latter approach has been treated without consideration of the ill-posedness. The inclusion of ill-posedness in the approach leads to its specification which we call the ansatz method. By showing that a certain class of ansatz functions cannot be used for describing the total isotherms, we were urged to consider more general solutions being connected with the Stieltjes integrals. After applying a general inversion formula we can restrict the theoretically possible total isotherms and outline a feasible general ansatz.