基于改进电极敏感场的ECT图像重建算法研究

针对目前电容层析成像技术中重建图像质量有待提高的问题,对该技术正问题和反问题的改进方法进行了研究。通过将电极数目由传统的8电极增加至12电极来增加投影数据,从而改善图像重建的欠定性,并且在12电极敏感阵列的基础上对其灵敏度矩阵进行了均值滤波的改进处理,基于处理后的灵敏度矩阵对经典图像重建算法LBP算法和Landweber迭代算法进行了改进,仿真研究结果表明,基于敏感场滤波处理后的两种算法较之于原始算法成像精度明显提高。且两种算法中,改进后的Landweber迭代法成像效果更好。     

在ECT图像重建中有效使用图像融合技术

电容层析成像技术中图像重建的算法众多,这些算法各有其优势及不足如LBP算法简单、速度快,但成像质量较差;正则法较为多的加入了人为的因素;投影Landweber迭代法稳定性好,但需要大量迭代应用性不强。本文在吸取几种算法的优势采用小波变换融合的方法基于图像的局部能量,在图像重建中恰当的使用融合规则,提高成像质量和效率。     

基于Landweber迭代的图像重建算法

本文尝试将一种新型的基于Landweber迭代算法用于电阻抗断层图像(EIT)重建。该算法与线性反投影算法不同,Landweber算法可以明显地改进图像质量。仿真结果表明,它不仅可以消除噪声干扰,而且能加快收敛速度。     

电容层析成像图像重建算法对比

图像重建算法在电容层析成像技术的实际应用中起着至关重要的作用。针对图像重建算法的研究,文中将线性反投影法、奇异值分解法、代数重建算法、Landweber算法、Tikhonov正则化算法的基本原理进行对比。基于MATLAB仿真平台对4种多相流流型进行仿真,并从图像误差、相关系数、计算时间3个方面对比重建图像的效果。分析结果表明,直接算法的图像重建速度优于迭代算法,但其图像重建质量劣于迭代算法。     

一种基于压缩感知的信号重建新算法

在求解基追踪问题的线性化Bregman迭代方法基础上,结合了广义逆的迭代技术得到一种稀疏信号重构的新算法。该算法在计算Moore-Penrose广义逆时,采用了迭代计算的方式,与算法本身相结合使得仅有矩阵向量乘积运算,避免了奇异值分解的较大工作量。通过数值试验可知,新算法相对线性化Bregman算法在计算时间上约减少了2/3,同时信号的恢复效果也是稳定有效的。因此,新算法是一种有效可行的信号重建算法。     

一种基于压缩感知的信号重建新算法

在求解基追踪问题的线性化Bregman迭代方法基础上,结合了广义逆的迭代技术得到一种稀疏信号重构的新算法。该算法在计算Moore-Penrose广义逆时,采用了迭代计算的方式,与算法本身相结合使得仅有矩阵向量乘积运算,避免了奇异值分解的较大工作量。通过数值试验可知,新算法相对线性化Bregman算法在计算时间上约减少了2/3,同时信号的恢复效果也是稳定有效的。因此,新算法是一种有效可行的信号重建算法。     

改进的稀疏近似逆预条件算法求解电磁场边值问题

提出了一种MAINV稀疏近似逆预条件算法,用于改善电磁场边值问题的有限元分析所产生的的线性系统的迭代求解。该预条件子是在基本AINV算法基础上,在分解过程中对可能导致算法崩溃的极小主元进行实时补偿,从而获得高质量的预条件子。数值结果表明,MAINV预条件子对SQMR以及若干经典迭代法的加速效果十分明显;此外,与其他常规预条件子相比较,MAINV具有更好的求解性能。     

正则化一步动态重建算法在磁感应成像中的应用

磁感应成像是对生物组织的电导率进行图像重建的一种方法,高斯牛顿方法通过不断迭代并重新计算灵敏度矩阵进行非线性图像重建,精度高但耗时较长.结合正则化技术,提出高斯牛顿一步动态重建算法,通过实验获得了相关参数的最优解.基于正问题的数学模型,建立磁感应成像测量模型,利用有限元方法求解,所得到的灵敏度矩阵和磁矢势应用于逆问题中...     

基于稀疏度自适应压缩感知的电容层析成像图像重建算法

为提高电容层析成像(ECT)系统重建图像的质量,该文提出一种基于改进稀疏度自适应的压缩感知电容层析成像算法。利用压缩感知与电容层析成像算法的契合点,以随机改造后的电容层析成像灵敏度矩阵为观测矩阵,离散余弦基为稀疏基,测量电容值为观测值,建立模型。利用线性反投影算法(LBP算法)所得图像预估原始图像稀疏度,以预估稀疏度值作为索引原子初始值进行稀疏度自适应迭代。改进后的稀疏度自适应匹配追踪重构算法实现ECT图像重建,解决了稀疏度预估不准确导致重建图像精度差的问题。仿真实验结果表明,该算法可以有效重建ECT图像,其成像质量优于LBP算法、Landweber算法、Tikhonov算法等传统算法,是研究电容层析成像图像重建的一种新的方法和手段。     

ART算法的平均值法改进方案

二维断层成像中,代数重建(ART)算法面临的最大问题就在于计算量大、重建速度慢。针对这个劣势,提出了一种使用平均值法改进的ART算法,希望能更快地重建出质量较好的图像。该算法将每一次迭代过程的所有中间值记录下来,并求出其平均值,将此平均值作为下一次迭代的初始值。经过实验证明这种改进后的ART算法经过更少的迭代次数后就能达到较好的重建质量,且质量比传统算法还要好。     

语音重构的DCT域加速Landweber迭代硬阈值算法

重构信号的最基本理论依据是该信号在某个变换域是稀疏的或近似稀疏的。基于语音信号在DCT域的近似稀疏性,可以采用压缩感知(Compressed Sensing, CS)理论对其进行重构。压缩感知理论中的迭代硬阈值(Iterative hard thresholding, IHT)算法以其较好的性能被广泛用来重构信号,但其收敛速度比较慢,如何提高收敛速度,一直是迭代硬阈值算法研究的重点之一。针对压缩感知理论中的IHT算法收敛速度相当慢的问题,提出了语音重构的DCT域加速Landweber迭代硬阈值(Accelerated Landweber iterative hard thresholding, ALIHT)算法。该算法对原始语音信号做DCT变换,然后在DCT域将每一步Landweber迭代分解为矩阵计算和求解两步,通过修改其中的矩阵计算部分实现Landweber迭代加速,最后通过迭代硬阈值对信号做阈值处理。实验结果表明,加速Landweber迭代硬阈值算法加快了收敛速度、减少了计算量。      

基于压缩感知的电容层析成像图像重建算法

为提高电容层析成像（ECT）系统采样速率及重建图像质量,本文提出一种基于压缩感知理论的ECT图像重建算法.首先,应用离散Fourier变换基将原始图像灰度信号进行稀疏化处理;接着,从16电极ECT系统中随机选取14个电极按随机顺序进行激励,并按随机顺序测量不同电极之间电容值,得到测量电容信号并建立相应的观测矩阵;最后,采用L1范数正则化模型和原对偶内点法实现图像重建.仿真实验结果表明,基于压缩感知理论算法重建的图像其质量优于Landweber迭代算法,在节省采样时间的同时可实现较高精度的图像重建,为ECT图像重建的研究提供了一种新的手段.     

A Hybrid Reconstruction Algorithm for 3-D Ionospheric Tomography

In this paper, a hybrid reconstruction algorithm (HRA) is presented to solve the ill-posed inverse problem associated with 3-D ionospheric stochastic tomography. In this new method, the ionospheric electron density (IED) can be inverted by using two steps. First, a truncated singular value decomposition (TSVD) method, whose value is independent on any initial estimation, is used to resolve the ill-posed problem of the tomography system. Second, taking into account the "approximation" of its solution, an iterative improvement process of the solution is then implemented by utilizing the conventional algebraic reconstruction algorithm (ART). The HRA, therefore, offers a more reasonable approach to choose an initial approximate for the ART and to improve the quality of the final reconstructed image. A simulated experiment demonstrates that the HRA method is superior to the TSVD or the ART alone for the tomographic inversion of IED. Finally, the HRA is used to perform GPS-based tomographic reconstruction of the IED at mid- and low-latitude regions.     

A Novel Finite-Element-Based Algorithm for Fluorescence Molecular Tomography of Heterogeneous Media

The knowledge of optical properties distribution of heterogeneous media has significant impact on the reconstructed fluorescence image quality in fluorescence molecular tomography (FMT). In this study, a novel finite-element-based algorithm for FMT of heterogeneous media is proposed. In the algorithm, optical properties are reconstructed using the conjugate gradient method. A modified method based on reverse differential scheme is deduced for calculating the gradient when the detector points are not restricted on boundary nodes. With the recovered optical properties, linear relationship between known surface measurements of emission light and unknown fluorescence yield is then obtained. FMT reconstruction is implemented by combining algebraic reconstruction technique (ART) and Landweber iteration method. With initial value provided by ART, Landweber iteration method improves the quantification smoothly with small step length between neighboring iterations. The algorithm was evaluated using phantoms of different heterogeneity configurations. Results show that the reconstructed fluorescence yield is insensitive to various degrees of heterogeneity for the proposed algorithm. In contrast, when assuming homogeneous optical properties, it shows that more underestimation of optical properties results in more underestimation of the reconstructed fluorescence yield. Fast computation speed of the proposed algorithm is also demonstrated in this study.     

Numerical study of multigrid implementations of some iterative image reconstruction algorithms

The numerical behavior of multigrid implementations of the Landweber, generalized Landweber, ART, and MLEM iterative image reconstruction algorithms is investigated. Comparisons between these algorithms, and with their single-grid implementations, are made on two small-scale synthetic PET systems, for phantom objects exhibiting different characteristics, and on one full-scale synthetic system, for a Shepp-Logan phantom. The authors also show analytically the effects of noise and initial condition on the generalized Landweber iteration, and note how to choose the shaping operator to filter out noise in the data, or to enhance features of interest in the reconstructed image. Original contributions include (1) numerical studies of the convergence rates of single-grid and multigrid implementations of the Landweber, generalized Landweber, ART, and MLEM iterations and (2) effects of noise and initial condition on the generalized Landweber iteration, with procedures for filtering out noise or enhancing image features     

Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix

The generalized Landweber iteration with a variable shaping matrix is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography. The method is based on the property that once a spatial frequency image component is almost recovered within in in the generalized Landweber iteration, this component will still stay within in during subsequent iterations with a different shaping matrix, as long as this shaping matrix satisfies the convergence criterion for the component. Two different shaping matrices are used: the first recovers low-frequency image components; and the second may be used either to accelerate the reconstruction of high-frequency image components, or to attenuate these components to filter the image. The variable shaping matrix gives results similar to truncated inverse filtering, but requires much less computation and memory, since it does not rely on the singular value decomposition.     

Necessary and Sufficient Convergence Conditions for Algebraic Image Reconstruction Algorithms

The Landweber scheme is an algebraic reconstruction method and includes several important algorithms as its special cases. The convergence of the Landweber scheme is of both theoretical and practical importance. Using the singular value decomposition (SVD), we derive an iterative representation formula for the Landweber scheme and consequently establish the necessary and sufficient conditions for its convergence. In addition to verifying the necessity and sufficiency of known convergent conditions, we find new convergence conditions allowing relaxation coefficients in an interval not covered by known results. Moreover, it is found that the Landweber scheme can converge within finite iterations when the relaxation coefficients are chosen to be the inverses of squares of the nonzero singular values. Furthermore, the limits of the Landweber scheme in all convergence cases are shown to be the sum of the minimum norm solution of a weighted least-squares problem and an oblique projection of the initial image onto the null space of the system matrix.