基于改进反余切函数的近似L0范数的重构算法

重构算法是压缩感知理论应用于实际的关键。其中 ,近似L0范数算法是通过选取一个 连续的平滑函数近似逼近L0范数,从而将离散的最小化L0范数问题转为平滑函数求最优值问 题。针对现有算法精度不高的缺点,采用了一种逼近程度更高的改进反余切函数族来近 似L0范数,并采用修正阻尼牛顿法求解。该算法结合了近似零范数算法的高收敛性和牛顿法 的高效寻优,获得了精度较高的重构信号。仿真实验表明,在不同压缩比下,该算法在一维 信号重建和二维图像重建的过程中,较SL0算法、NSL0算法和AL0算法的信噪比和重构精度都 有了较大的提升,提高了同等条件下信号恢复的质量,有效地改善了重建效果。     

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.     

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.     

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。     

低剂量CT的线性Bregman迭代重建算法

针对降低 X 线源管电流来减少辐射剂量的实现方案所引起的投影图像低信噪比的情况,该文提出一种新的低剂量CT图像重建模型。总的优化目标函数采用泊松噪声的负对数似然函数作为数据保真项,采用待重建图像的稀疏性先验信息作为正则项。保真项能够克服加性高斯模型不能有效刻画噪声性质的缺点,正则化项能够改善测量低信噪比所引起的不适定性。求解过程中采用线性化Bregman迭代格式,将原目标函数分解为变系数的2次优化问题和稀疏性先验去噪问题,其中的2次优化问题中的2次项系数采用变系数计算,能够更好地逼近原始的保真项,从而加快收敛速度。在低剂量扇形束成像的条件下,对仿真模型进行了数值试验,并同传统的滤波反投影算法、极大似然算法和加权2范数重建算法进行了比较,验证了该文算法的有效性。     

竞争失效产品步进加速寿命试验的优化设计

对weibull分布竞争失效产品的步进加速寿命试验进行优化设计,首先选取产品正常应力下中位寿命的极大似然计估渐近方差的估计值作为优化目标函数,并对优化目标函数进行统计推断.然后利用目标函数的连续性,提出基于离散数据的函数拟合方法,将试验优化设计转化为显函数的约束极值求解问题,同时将智能优化算法应用到步进加速寿命试验的优...     

用于压缩感知信号重建的SL0改进算法

SL0算法是一种基于近似l₀范数的压缩感知信号重建算法,其思想是用一个光滑函数来近似l₀范数,然后求解一个优化问题。目前采用的光滑函数都是高斯函数族,文中突破了以往采用高斯函数族近似l₀范数,提出了采用复合三角函数作为近似估计l₀范数的函数,然后结合修正牛顿法和阻尼牛顿法提出一种更精确的重建算法DNSL0。实验结果表明,在相同测试环境下,DNSL0算法在峰值信噪比和匹配度方面比SL0算法和NSL0算法都有了大幅提高。     

基于截断奇异值的镜像综合孔径亮温重建方法

镜像综合孔径(MAS)辐射计的图像重建是由余弦可见度函数到场景亮温的图像反演过程,余弦可见度函数由转移方程求解得到.而转移方程为不适定方程组,相关输出中一个较小的误差,都可能引起求解的余弦可见度函数存在较大偏离.因此,对这个不适定方程组的求解是整个亮温重建算法成功的关键.该文基于镜像综合孔径的基本原理,分析转移矩阵的病态性,将截断奇异值分解应用于转移方程的求解问题中.仿真与实验表明,该方法可以有效降低噪声,提升图像质量.     

一种改进的TV图像重建算法

针对当前稀疏角度下有限角图像重建过程中,边界部分出现伪影,降低了图像重建质量的缺陷。文中提出了一种新的ART+TV算法,该方法是在原始TV算法的基础上进行改进。原始TV梯度下降算法求解目标函数最小值时,使用固定函数作为目标函数,文中对其进行更改,采用带参数的目标函数,并对TV重建后的结果进行自适应步长修正,加速图像收敛。与传统的ART+TV算法相比,文中算法在不改变重建速度的基础上,且在少量迭代次数下,能重建出质量更高的图像,抑制图像伪影。     

基于截断奇异值的镜像综合孔径亮温重建方法

镜像综合孔径(MAS)辐射计的图像重建是由余弦可见度函数到场景亮温的图像反演过程,余弦可见度函数由转移方程求解得到。而转移方程为不适定方程组,相关输出中一个较小的误差,都可能引起求解的余弦可见度函数存在较大偏离。因此,对这个不适定方程组的求解是整个亮温重建算法成功的关键。该文基于镜像综合孔径的基本原理,分析转移矩阵的病态性,将截断奇异值分解应用于转移方程的求解问题中。仿真与实验表明,该方法可以有效降低噪声,提升图像质量。     

The Use of Filtering Methods to Compensate for Constant Attenuation in Single-Photon Emission Computed Tomography

A back projection of filtered projection (BKFIL) reconstruction algorithm is presented that is applicable to single-photon emission computed tomography (ECT) in the presence of a constant attenuating medium such as the brain. The filters used in transmission computed tomography (TCT)-comprised of a ramp multiplied by window functions?are modified so that the single-photon ECT filter is a function of the constant attenuation coefficient. The filters give good reconstruction results with sufficient angular and lateral sampling. With continuous samples the BKFIL algorithm has a point spread function that is the Hankel transform of the window function. The resolution and statistical properties of the filters are demonstrated by various simulations which assume an ideal detector response. Statistical formulas for the reconstructed image show that the square of the percent-root-mean-square (percent-rms) uncertainty of the reconstruction is inversely proportional to the total measured counts. The results indicate that constant attenuation can be compensated for by using an attenuation-dependent filter that reconstructs the transverse section reliably. Computer time requirements are two times that of conventional TCT or positron ECT and there is no increase in memory requirements.     

放射CT重建的平均场技术

本文引用了一种图像分布的先验模型，在这种先验模型中引入了两个边界模型，称为组合马尔柯夫随机场模型，用Ｂａｙｅｓ定理将其与放射ＣＴ（ＥＣＴ）问题相结合构造出后验概率，由于这个最大后验估计问题是一个非凸问题，本文采用平均场退火技术对其进行分析，将统计松弛方程转化为一组确定性迭代式，计算机进行的模拟实验证实了这种算法的有效性。     

基于小波域滤波的迭代硬阈值压缩感知重构

图像压缩感知迭代重构算法主要采用迭代阈值法解决信号的重构问题,但是迭代阈值法仅仅利用变换系数进行阈值处理,并未考虑系数的邻域统计特性,导致重构性能不高。提出一种基于小波域滤波的迭代硬阈值迭代算法,利用小波域系数的邻域统计特性修订迭代硬阈值重构算法的代价函数,进行两步迭代收缩,并在迭代中用小波域滤波除去其中的重构噪声。实验结果表明,在相同的观测数据下,相比已有的经典算法,新算法的重构图像质量较高,并且可以获得快速的重构速度。     

A row-action alternative to the EM algorithm for maximizing likelihood in emission tomography

The maximum likelihood (ML) approach to estimating the radioactive distribution in the body cross section has become very popular among researchers in emission computed tomography (ECT) since it has been shown to provide very good images compared to those produced with the conventional filtered backprojection (FBP) algorithm. The expectation maximization (EM) algorithm is an often-used iterative approach for maximizing the Poisson likelihood in ECT because of its attractive theoretical and practical properties. Its major disadvantage is that, due to its slow rate of convergence, a large amount of computation is often required to achieve an acceptable image. Here, the authors present a row-action maximum likelihood algorithm (RAMLA) as an alternative to the EM algorithm for maximizing the Poisson likelihood in ECT. The authors deduce the convergence properties of this algorithm and demonstrate by way of computer simulations that the early iterates of RAMLA increase the Poisson likelihood in ECT at an order of magnitude faster that the standard EM algorithm. Specifically, the authors show that, from the point of view of measuring total radionuclide uptake in simulated brain phantoms, iterations 1, 2, 3, and 4 of RAMLA perform at least as well as iterations 45, 60, 70, and 80, respectively, of EM. Moreover, the authors show that iterations 1, 2, 3, and 4 of RAMLA achieve comparable likelihood values as iterations 45, 60, 70, and 80, respectively, of EM. The authors also present a modified version of a recent fast ordered subsets EM (OS-EM) algorithm and show that RAMLA is a special case of this modified OS-EM. Furthermore, the authors show that their modification converges to a ML solution whereas the standard OS-EM does not.     

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.     

Improved iterative image reconstruction with automatic noise artifact suppression

A method for stabilizing iterative image reconstruction techniques has been developed for improving the image quality of position emission tomography. A damping matrix is introduced, which suppresses noisy correction on a pixel-by-pixel basis, depending on the statistical precision of the iterative correction. The precision is evaluated by comparing a certain number of correction submatrices, each of which is formed from a subset of the projection data. Simulation studies showed that statistical noise is effectively suppressed, while the image of the source object is reconstructed with high resolution, as long as the signal level is higher than the local noise level. In the application to the MLE (maximum likelihood estimator), the minimum RMS error of the image was reduced to 84% for 500 k total counts, and the RMS error increased more slowly with further iterations as compared with the simple MLE. The method was also applied to the FIR (filtered iterative reconstruction) algorithm, and the images were found to be better than those obtained by the convolution backprojection method.     

Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography

An image reconstruction method motivated by positron emission tomography (PET) is discussed. The measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise. The authors set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability (MAP) formulation of the problem. An iterative approach which requires the solution of simple quadratic equations is proposed. The authors also present a methodology which allows them to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing. The new MAP algorithm is compared to a method which maximizes likelihood and with two variants of the filtered backprojection method.     

Minimax emission computed tomography using high-resolutionanatomical side information and B-spline models

In this paper a minimax methodology is presented for combining information from two imaging modalities having different intrinsic spatial resolutions. The focus application is emission computed tomography (ECT), a low-resolution modality for reconstruction of radionuclide tracer density, when supplemented by high-resolution anatomical boundary information extracted from a magnetic resonance image (MRI) of the same imaging volume. The MRI boundary within the two-dimensional (2-D) slice of interest is parameterized by a closed planar curve. The Cramer-Rao (CR) lower bound is used to analyze estimation errors for different boundary shapes. Under a spatially inhomogeneous Gibbs field model for the tracer density a representation for the minimax MRI-enhanced tracer density estimator is obtained. It is shown that the estimator is asymptotically equivalent to a penalized maximum likelihood (PML) estimator with resolution-selective Gibbs penalty. Quantitative comparisons are presented using the iterative space alternating generalized expectation maximization (SAGE-FM) algorithm to implement the PML estimator with and without minimax weight averaging     

Electronic Noise Modeling in Statistical Iterative Reconstruction

We consider electronic noise modeling in tomographic image reconstruction when the measured signal is the sum of a Gaussian distributed electronic noise component and another random variable whose log-likelihood function satisfies a certain linearity condition. Examples of such likelihood functions include the Poisson distribution and an exponential dispersion (ED) model that can approximate the signal statistics in integration mode X-ray detectors. We formulate the image reconstruction problem as a maximum-likelihood estimation problem. Using an expectation-maximization approach, we demonstrate that a reconstruction algorithm can be obtained following a simple substitution rule from the one previously derived without electronic noise considerations. To illustrate the applicability of the substitution rule, we present examples of a fully iterative reconstruction algorithm and a sinogram smoothing algorithm both in transmission CT reconstruction when the measured signal contains additive electronic noise. Our simulation studies show the potential usefulness of accurate electronic noise modeling in low-dose CT applications.