求解大规模线性离散不适定问题的RRArnoldi-Fractional Tikhonov正则化算法

不适定问题广泛出现在地球物理、自动控制等多种领域.正则化方法是求解此类问题近似解的有效算法.将Fractional Tikhonov正则化算法应用于投影算法,提出了求解大规模线性离散不适定问题的Arnoldi-Fractional Tikhonov正则化算法.进一步提出限制值域的Arnoldi-Fractional Tikhonov正则化算法.并针对经典算例,进行了数值试验和比较.数值试验结果表明了新算法是有效且具有优势的.     

实际问题的图象化

<正> 图象化是将实际问题直观化的一种常用方法,在近几年的中考题中较为常见.此类问题既能体现数学在日常生活中的广泛应用,又反映了素质教育的要求.下面就来谈谈这类图象化问题. 一、观察横纵坐标,了解其意义看清楚横纵坐标各表示什么量,图中线段的出发点和终止点分     

用正则化方法求抛物型方程的数值解

利用吉洪诺夫正则化方法,讨论了问题(1)中源密度函数f的求解问题,并给出稳定化的数值解.     

基于加权低分辨率图像的自适应正则化图像重建

图像重建是一个病态问题,需要应用逆过程获得原始图像的近似估计。亚像素配准虽在图像重建过程中发挥了重要作用,但难以获得准确值。提出一种自适应图像重建迭代算法和基于加权低分辨率图像的Tikhonov正则化参数的自适应估计方法。权重系数保持了每个低分辨率图像的逼真度,而正则化系数则控制了图像平滑度。实验结果表明,此算法无论在客观测量还是在视觉评价上,都优于传统的Tikhonov正则化方法。     

一类正则化方法的收敛速率

考虑了解不适定问题的迭代Tikhonov正则化方法的渐近收敛速率．采用对数度量作为广义解x^4的分类标准．对于数据没有或有误差的两种情形,都得到关于渐进收敛速率的相当精细的结论．     

大规模半定规划问题的正则化方法及收敛性

为了改进求解大规模约束条件的半定规划问题的方法.首先通过经典的二次正则法,将一般的半定规划问题(SDP)的标准形式进行形式的转化.然后通过研究转化后问题的最优性条件,给出了求解一般的半定规划问题的正则化算法及其收敛性证明.在实际中,处理大规模约束条件的半定规划问题(SDP)时,该方法表现出很好的性能.     

用正则化方法求一类Abel型积分方程数值解

本文利用吉洪诺夫正则化方法 ,线性插值给出了Abel型积分方程反问题的稳定化数值方法     

磨光化方法在数值微分中的应用

考虑一类求解数值微分问题的稳定化算法——磨光化方法,本文分别在2种范数(∞范数和L²范数)下得到了磨光核函数的通用选取准则以及相应近似导数的误差估计,并给出了磨光核函数的2种具体取法.最后,通过数值算例说明了求解数值微分问题的磨光化方法的数值有效性.     

数字图像处理课程教学中成像逆问题的正则化处理方法初探

成像逆问题是数字图像处理课程的重要内容,该问题的研究近年来获得了快速发展,但现有教材中成像逆问题的内容多局限于基本理论、基本方法,涉及其最新研究进展的不多,内容讲授存在一定的"照本宣科"现象。针对此,试介绍成像逆问题基本内容、建模表示及研究进展,然后对成像逆问题当前常见的正则化处理方法进行初步探讨,最后通过实验展示某些方法的处理效果,以有助于数字图像处理课程教学活动的开展,帮助学生深入理解成像逆问题等内容。     

Laplace方程Cauchy问题的修正Tikhonov正则化方法

文中考虑了矩形区域上一个Laplace方程的Cauchy问题.对时的Cauchy数据,以及y=0x=0,x=π时的边界数据均已给出,要求0相似文献   

基于多级BP神经网络的EIT阻抗变化位置的确定

Electrical impedance tomography (EIT) is a new computer tomography technology, which reconstructs an impedance (resistivity, conductivity) distribution, or change of impedance, by making voltage and current measurements on the object's periphery. Image reconstruction in EIT is an ill-posed, non-linear inverse problem. A method for finding the place of impedance change in EIT is proposed in this paper, in which a multilevel BP neural network (MBPNN) is used to express the non-linear relation between the     

Lung ventilation functional monitoring based on electrical impedance tomography

Medically,electrical impedance tomography(EIT)is a relatively inexpensive,safe,non-invasive and portable technique compared with computerized tomography(CT)and magnetic resonance imaging(MRI).In this paper,EIT_TJU_Ⅱ system is developed including both the data collection system and image reconstruction algorithm.The testing approach of the system performance,including spatial resolution and sensitivity,is described through brine tank experiments.The images of the thorax physical model verify that the system can reconstruct the interior resistivity distribution.Finally,the lung ventilation functional monitoring in vivo is realized by EIT,and the visualized images indicate that the configuration and performance of EIT_TJU_Ⅱ system are feasible and EIT is a promising technique in clinical monitoring application.     

基于直接寻找法的电阻抗断层成像

Solution to impedance distribution in electrical impedance tomography （EIT） is an ill-posed nonlinear inverse problem. It is especially difficult to reconstruct an EIT image in the center area of a measured object. Tikhonov regularization with some prior information is a sound regnlarization method for static electrical impedance tomography under the condition that some true impedance distribution information is known a priori. This paper presents a direct search method （DSM） as pretreatment of image reconstruction through which one not only can construct a regularization matrix which may locate in areas of impedance change, but also can obtain an initial impedance distribution more similar to the true impedance distribution, as well as better current modes which can better distinguish the initial distribution and the true distribution. Simulation results indicate that, by using DSM, resolution in the center area of the measured object can be improved significantly.     

Electrode models in electrical impedance tomography

INTRODUCTION This paper presents different views on electrode modelling in electrical impedance tomography (EIT), which include electric field electrode models—the conventional approach for modelling electrode ge- ometry, electrochemistry electrode models for mod- elling the effects of electrode-electrolyte interface, and the electrode measurement models for modelling the sensing system in the terms of the electronic measurements. Taking the full electrode models into consideration of el…     

利用自适应网格细分法的电阻抗成像

1 Introduction Electrical i mpedance tomography (EIT) is a non-in-vasive i maging technique with widespread applicationsin medicine and industry[1 ,2].In EITthe electric cur-rent is injected between all possible pairs of adjacentelectrodes , and voltage is measured among all otherelectrodes and a voltage reference electrode .Based onthese boundary measurements ,the internal resistivity(or conductivity) distribution of the body can be esti-mated using the boundary voltage based on various re-…     

Time series of EIT measurements and images during lung ventilation based on principal component analysis

The aim of this paper is to propose a useful method for exploring regional ventilation and perfusion in the chest and also separation of pulmonary and cardiac changes.The approach is based on estimating both electrical impedance tomography(EIT) measurements and reconstructed images by means of principal component analysis(PCA).In the experiments in vivo,43 cycles of heart-beat rhythm could be detected by PCA when the volunteer held breath;9 breathing cycles and 50 heart-beat cycles could be detected by PCA ...     

基于图像复原的规整化方法研究

图像降噪与图像去模糊方法研究在众多专业领域都具有重要的研究意义。去模糊问题是一个图像估计问题,处理这个问题的一般框架是规整化,本文研究了图像复原问题的典型规整化方法。     

Computed tomography using level set method and algebraic reconstruction technique

In this paper, a novel reconstruction technique based on level set method and algebraic reconstruction technique is proposed for multiphase flow computed tomography (CT) system. The curvature-driven noise reduction method is inserted into the conventional iteration procedure of algebraic reconstruction technique to improve the image quality and convergence speed with limited projection data. By evolving the image as a set of iso-intensity contours after each updation, the sufficient number of iterations for acceptable results is reduced by 80%-90%, while the image quality is enhanced obviously. Quantitative evaluation of image quality is given by using both relative image error and correlation coefficient. The resultant images can be utilized to detect flow regimes for monitoring industrial multiphase flow. Laboratory results demonstrate the feasibility of the proposed method. Phantoms of four typical flow regimes can be reconstructed from few-view projection data efficiently, and the corresponding image errors and correlation coefficients are acceptable for the cases tested in this paper.     

Improve Spatial Resolution of Electrical Impedance Tomography Image Based on Non-uniformity Fine Mesh

1 IntroductionIll electrical impedance tomography (EIT) an ~ ofelectrodes (for example, 16, 32 or 64 electrodes) isattached around the Object. Small alternating current areinjected into these electrodes, and the resulting voltagesare measured on the surface. Usually, Two of theelectrodes are used to inject a constallt-aml)litudesinusoidal current, and the others measure the voltagedeveloped on them. An image reconstrUchon algorithm isaPPlied tO the measured data to Produce a cross-sectiona…     

一种DDR信号阻抗匹配的新方法

DDR信号的阻抗匹配一般有两种方法:源端增加串联电阻和终端增加并联电阻。这两种方法各有利弊。其中源端串阻匹配会增加单板PCB的布板面积,终端并联匹配则会增加单板的功耗。本文则采用并联电容来替代并联电阻,这样即可以解决PCB布板面积的问题,也可以解决单板机功耗增加的问题,是DDR信号匹配的一种新方法。