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。     

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。      

基于改进Gauss-Newton的电容层 析成像图像重建算法

 针对电容层析成像技术中的"软场"效应和病态问题,在分析Gauss-Newton算法基本原理的基础上,提出了一种基于Gauss-Newton新的电容层析成像算法,采用奇异值分解定理对算法的稳定性进行了证明.在此基础上探讨了ECT应用该算法的可行性,算法满足收敛条件且重建图像误差小.仿真和实验结果表明,该算法和LBP、Landweber和共轭梯度算法相比,算法兼备成像质量高、稳定性好等优点,为ECT图像重建算法的研究提供了一个新的思路.     

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。     

图像恢复的小波域加速Landweber迭代阈值方法

该文利用对忠诚项的二次逼近方法,提出了一种小波域加速Landweber迭代阈值算法。该算法的每次迭代是对前两次迭代结果的线性组合做阈值处理。与标准的迭代阈值算法相比,该方法收敛速度更快。由于参数的可选择性,新算法更有灵活性。数值实验表明新算法能够有效地提高恢复图像的质量,是一种行之有效的图像恢复方法。     

电阻抗断层图像重建算法研究——预迭代算法提出

本文分析了Landweber法与广义逆的关系,通过理论推导,证实Landweber 法实际上是用迭代法构造广义逆矩阵的一种变形,解释了Landweber法多次迭代后的成像结果与广义逆最小模解类似的现象,在此基础上,提出一种新的重建算法——预迭代法,将重建过程分为离线预迭代及在线一步成像,明显提高了成像速度。     

基于改进Landweber算法的光学层析成像研究

光学层析成像技术由于其非接触性、结构简单、采样率高、安全性高、分辨率高等特性，在工业流体监测以及医学等领域得到广泛应用，同时在学术领域上也具有很高的研究价值。光学层析成像分为扫描阶段和图像重建阶段。在重建过程中，算法的性能往往决定着图像重建的质量。鉴于现有重建算法存在重建速度慢与图像质量不高等问题，提出一种基于预置矩阵的Landweber重建算法。该算法通过引入历史迭代信息、在迭代过程中添加预置矩阵和加速项而加快迭代速度，减小重建图像与真实图像的误差。对圆形测量场内5个特定分布进行实验仿真，对比所提改进算法与传统算法的性能。仿真结果显示，该算法的重建误差在5%左右，同时证实该改进算法相较于传统算法有显著性能提升，重建误差降低48%，图像质量得到显著提升。     

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。     

Kalman滤波在ERT图像重建中的仿真研究

ERT是以电导敏感场机理为原理的过程层析成像技术。通过COMSOL有限元软件实现对被测场域的二维建模和敏感场快速求解的仿真研究,提出一种利用Kalman滤波进行ERT图像重建的方法。针对三种典型电导率分布进行仿真实验,经与LBP算法、Landweber算法的比较,得出Kalman滤波算法成像的图像误差最小、相关系数最佳,也证明了Kalman滤波是一种精度高、噪声干扰有较好鲁棒性的图像重建算法。     

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。     

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     

基于Contourlet域分块压缩感知的图像融合

针对传统图像融合方法导致纹理细节丢失的现象,提出了一种基于抗混叠移不变Contourlet域的分块压缩感知（block-based compressed sensing,BCS）图像融合算法——Contourlet_BCS。把善于表达图像纹理及边缘信息的Contourlet变换引入了压缩感知稀疏表示中,同时对分解得到的低频系数采取加权的区域能量融合规则,高频系数采取基于广义高斯分布模型的加权融合规则进行图像系数融合,最后在压缩感知框架下利用带平滑处理的投影Landweber算法重构。实验结果表明,Contourlet_BCS融合效果优于传统方法,融合的图像纹理清晰,边缘细节信息更为丰富。     

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.     

Acceleration of Landweber-type algorithms by suppression of projection on the maximum singular vector

A procedure that speeds up convergence during the initial stage (the first 100 forward and backward projections) of Landweber-type algorithms, for iterative image reconstruction for positron emission tomography (PET), which include the Landweber, generalized Landweber, and steepest descent algorithms, is discussed. The procedure first identifies the singular vector associated with the maximum singular value of the PET system matrix, and then suppresses projection of the data on this singular vector after a single Landweber iteration. It is shown that typical PET system matrices have a significant gap between their two largest singular values; hence, this suppression allows larger gains in subsequent iterations, speeding up convergence by roughly a factor of three.     

A fast thresholded landweber algorithm for wavelet-regularized multidimensional deconvolution.

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the l(1)-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alternating between a Landweber iteration and a wavelet-domain soft-thresholding operation. While having the advantage of simplicity, they are known to converge slowly. By expressing the cost functional in a Shannon wavelet basis, we are able to decompose the problem into a series of subband-dependent minimizations. In particular, this allows for larger (subband-dependent) step sizes and threshold levels than the previous method. This improves the convergence properties of the algorithm significantly. We demonstrate a speed-up of one order of magnitude in practical situations. This makes wavelet-regularized deconvolution more widely accessible, even for applications with a strong limitation on computational complexity. We present promising results in 3-D deconvolution microscopy, where the size of typical data sets does not permit more than a few tens of iterations.