基于基图像TV模型的CT射束硬化校正方法

X射线CT中,X射束硬化导致重建图像中出现伪影,严重影响了图像质量。论文深入分析了射束硬化对原始投影数据的影响,并提出了一种基于基图像TV模型的射束硬化校正方法。该方法首先依据射束硬化的物理特征建立了带有可调参数的初步校正模型;其次,在不同的可调参数条件下,原始投影数据经该模型预处理变换得到多组预处理投影序列;再次,分别对预处理投影序列进行重建得到一系列校正基图像;最后,将基图像的线性组合作为最终重建图像。其中,加权系数的最优解是以最终重建图像的全变分(Total Variation,TV)函数作为目标函数,通过迭代法求得。为验证该算法,对真实的铝柱体模和工业检测件进行了实验,结果表明,该算法对射束硬化引起的杯状和条状伪影均有显著的抑制效果。     

An iterative image reconstruction algorithm for SPECT

Properties of two algorithms for iterative reconstruction of SPECT images, LS-MLEM and LS-OSEM,are studied and compared with the ML-EM algorithm in this paper. By using projection data of heavy-noise, their effectiveness in improving SPECT image quality is evaluated. A phantom with hot and cold lesion is used in the investigation. The reconstructed images using LS-MLEM or LS-OSEM show that there is not a rapid increase in image noise,and the ＂best＂ estimate is assuming that the reconstructed images satisfy the statistical model. The major advantage of using LS-MLEM or LS-OSEM algorithm in SPECT imaging is in their ability to accurately control for heavy-noise. And LS-OSEM algorithm obviously improves the convergence rate.     

利用混合态分解算法提高重叠关联成像的质量

X射线重叠关联成像技术所采用的常规相位恢复迭代算法均把入射光视为完全相干的单色光(即单态入射光),把样品视为稳定平衡的(即单态样品),把实验过程中成像系统内所有光学元器件的响应视为固定不变的。然而在实际实验中,上述三个条件很难得到同时保证。在非理想的实验条件下,任何单态条件发生变化或者出现多重态混合,其造成的退相干效应均会使衍射图样变得模糊,严重降低利用单态相位恢复迭代算法获得的重建图像质量。为了消除各种来源的混合态效应的负面影响,本文利用多模式拓展重叠关联迭代引擎算法(Mm-e PIE)和子像素上采样拓展重叠关联迭代引擎算法(Us-e PIE)这两种不同的混合态分解算法对实验数据进行处理。重建结果表明,不同来源的混合态效应(退相干效应)的分解结果在重建探针函数和重建样品函数中均得到了体现,两种混合态分解算法均能够显著改善重建图像的质量。其中多模式算法Mm-e PIE在消除入射探针的非相干效应方面更胜一筹。     

Total variation regulated EM algorithm [SPECT reconstruction]

An iterative Bayesian reconstruction algorithm based on the total variation (TV) norm constraint is proposed. The motivation for using TV regularization is that it is extremely effective for recovering edges of images. This paper extends the TV norm minimization constraint to the field of SPECT image reconstruction with a Poisson noise model. The regularization norm is included in the OSL-EM (one step late expectation maximization) algorithm. Unlike many other edge-preserving regularization techniques, the TV based method depends one parameter. Reconstructions of computer simulations and patient data show that the proposed algorithm has the capacity to smooth noise and maintain sharp edges without introducing over/under shoots and ripples around the edges     

基于半扇束扫描的CT图像迭代重建算法

为解决探测器尺寸受限导致的CT图像重建区域面积受限以及X射线辐射剂量较大问题,提出一种半扇束扫描模式下的CT图像迭代重建算法。该算法将探测器水平偏置,稀疏角度下采集物体投影数据,利用ART-TV迭代算法对投影数据进行重建,达到预设迭代次数后,输出重建图像。实验结果表明:半扫描可扩大重建面积,降低探测器成本;利用迭代重建算法,降低剂量的同时重建优质CT图像。     

Compressed sensing and Otsu’s method based binary CT image reconstruction technique in non-destructive detection

This paper tries to address the problem of binary CT image reconstruction in non-destructive detection with an algorithm based on compressed sensing(CS) and Otsu's method, which could reconstruct binary CT image of test object from incomplete detection data. According to binary CT image characteristics, we employ Splitbregman method based on L1/2regularization to solve piecewise constant region reconstruction. To improve the reconstructed image quality from incomplete detection data, we utilize a priori knowledge and Otsu's method as the optimization constraint. In our study, we make numerical simulation to investigate our proposed method,and compare reconstructed results from different reconstruction methods. Finally, the experimental results demonstrate that the proposed method could effectively reduce noise and suppress artifacts, and reconstruct high-quality binary image from incomplete detection data.     

The EM imaging reconstruction method in γ-ray astronomy

The simpler imaging reconstruction methods used for γ-ray coded mask telescopes are based on correlation methods, very fast and simple-to-use but with limitations in the reconstructed image. To improve these results, other reconstruction methods have been developed, such as the maximum entropy methods or the Iterative Removal Of Sources (IROS). However, such kind of methods are slower and can be impracticable for very complex telescopes.In this paper we present an alternative image reconstruction method, based on an iterative maximum likelihood algorithm called the EM algorithm, easy to implement and that can be successfully used for not very complex coded mask systems, as is the case of the LEGRI telescope. This is the first time this algorithm has been applied in γ-ray astronomy.     

GPU梯度自适应SART图像重建算法

针对SART迭代重建算法所需投影数据量大且迭代时间长的问题,将TV算法引入SART中,动态调节梯度步长来加速算法的收敛性能,实现用少量投影数据重建出高质量的图像。为加快算法的执行速度,将SART-TV算法在GPU上并行加速。用SART算法和SART-TV算法对Shepp-Logan模型重建,仿真实验表明:在采样数据相同的情况下,SART-TV算法较SART算法可以重建出更好的图像,且基于GPU的SART-TV算法的迭代时间明显低于基于CPU的SART-TV算法。     

Imaging performance evaluation in depth-of-interaction PET with a new method of sinogram generation:A Monte Carlo simulation study

In conventional PET systems,the parallax error degrades image resolution and causes image distortion.To remedy this,a PET ring diameter has to be much larger than the required size of field of view(FOV),and therefore the cost goes up.Measurement of depth-of-interaction(DOI)information is effective to reduce the parallax error and improve the image quality.This study is aimed at developing a practical method to incorporate DOI information in PET sinogram generation and image reconstruction processes and evaluate its efficacy through Monte Carlo simulation.An animal PET system with 30-mm long LSO crystals and 2-mm DOI measurement accuracy was simulated and list-mode PET data were collected.A sinogram generation method was proposed to bin each coincidence event to the correct LOR location according to both incident crystal indices and DOI positions of the two annihilation photons.The sinograms were reconstructed with an iterative OSMAPEM(ordered subset maximum a posteriori expectation maximization)algorithm.Two phantoms(a rod source phantom and a Derenzo phantom)were simulated,and the benefits of DOI were investigated in terms of reconstructed source diameter(FWHM)and source positioning accuracy.The results demonstrate that the proposed method works well to incorporate DOI information in data processing,which not only overcomes the image distortion problem but also significantly improves image resolution and resolution uniformity and results in satisfactory image quality.     

OSEM算法在编码板成像中的应用

为提高γ辐射编码成像中MLEM算法在图像重建时的速度及质量,论文基于核医学ECT图像重建中的OSEM算法思想在图像重建时对编码成像所得投影数据进行分组,并采用精细采样平衡相关法的重建结果作为初值进行迭代。通过实验对该算法进行验证。实验表明:OSEM算法可以有效提高收敛速度,改善重建图像质量。在γ辐射编码成像中采用OSEM算法是有效且可行的。     

基于全变差和块秩的稀疏角度重建算法

针对少量角度的投影数据重建CT图像问题,将图像的全变差和块秩作为正则项,提出一种稀疏角度重建模型,并采用Bregman迭代算法重建图像。用模拟的投影数据进行了重建数据实验,实验结果表明本算法明显的提高了重建图像的精度和信噪比。同时还研究了基础图像块的大小对重建图像质量的影响。     

Derivative-Hilbert-Backprojection based image reconstruction from truncated projections in helical cone-beam CT

In helical cone-beam computed tomography(CT), Feldkamp-Davis-Kress(FDK) based image reconstruction algorithms are by far the most popular. However, artifacts are commonly met in the presence of lateral projection truncation. The reason is that the ramp filter is global. To restrain the truncation artifacts, an approximate reconstruction formula is proposed based on the Derivative-Hilbert-Backprojection(DHB) framework. In the method, the first order derivative filter is followed by the Hilbert transform. Since the filtered projection values are almost zero by the first order derivative filter, the following Hilbert transform has little influence on the projection values, even though the projections are laterally truncated. The proposed method has two main advantages. First, it has comparable computational efficiency and image quality as well as the conventional helical FDK algorithm for non-truncated projections. The second advantage is that images can be reconstructed with acceptable quality and much lower computational cost in comparison to the Laplace operator based algorithm in cases with truncated projections. To point out the advantages of our method, simulations on the computer and real data experiments on our laboratory industrial cone-beam CT are conducted. The simulated and experimental results demonstrate that the method is feasible for image reconstruction in the case of projection truncation.     

基于SART算法的CL硬化伪影校正方法研究

X射线薄板层析成像(CL)系统是一种针对板状构件的新型断层成像系统,该系统中存在射束硬化现象。本工作研究了一种基于SART算法的硬化伪影校正算法（SART-BHC算法）,通过对该算法的研究及对CL系统矩阵的计算,使该方法能应用于CL中。通过模拟与实验相结合的方式,利用蒙特卡罗方法获得CL投影的模拟数据,在实际CL中获得实验数据,然后利用SART-BHC与FPB算法对两种数据分别重建。结果表明,SART-BHC算法可应用于CL中,不需要任何先验知识,能很好地校正硬化伪影,并对层间混叠有抑制作用。     

Range Condition and ML-EM Checkerboard Artifacts

The expectation maximization (EM) algorithm for the maximum likelihood (ML) image reconstruction criterion generates severe checkerboard artifacts in the presence of noise. A classical remedy is to impose an a priori constraint for a penalized ML or maximum a posteriori probability solution. The penalty reduces the checkerboard artifacts and also introduces uncertainty because a priori information is usually unknown in clinic. Recent theoretical investigation reveals that the noise can be divided into two components: one is called null-space noise and the other is range-space noise. The null-space noise can be numerically estimated using filtered backprojection (FBP) algorithm. By the FBP algorithm, the null-space noise annihilates in the reconstruction while the range-space noise propagates into the reconstructed image. The aim of this work is to investigate the relation between the null-space noise and the checkerboard artifacts in the ML-EM reconstruction from noisy projection data. Our study suggests that removing the null-space noise from the projection data could improve the signal-to-noise ratio of the projection data and, therefore, reduce the checkerboard artifacts in the ML-EM reconstructed images. This study reveals an in-depth understanding of the different noise propagations in analytical and iterative image reconstructions, which may be useful to single photon emission computed tomography, where the noise has been a major factor for image degradation. The reduction of the ML-EM checkerboard artifacts by removing the null-space noise avoids the uncertainty of using a priori penalty.     

Generalized flow pattern image reconstruction algorithm for electrical capacitance tomography

Successful applications of electrical capacitance tomography (ECT) depend on the speed and precision of the image reconstruction algorithms. In this paper, based on the semiparametric model, a generalized objective functional that considers the outliers in the measured capacitance data and the model error is proposed. A regularized combination minimax estimation is developed. An efficient algorithm, which integrates the advantages of the homotopy method where the homotopy equation is designed by the fixed-point homotopy and solved using the fixed-point iteration algorithm based on the alternate iteration scheme, the quantum particle swarm optimization algorithm that is coupled with the crossover and mutation operators, and the simulated annealing algorithm, is proposed. This algorithm is tested by the noise-free capacitance data and the noise-contaminated capacitance data, and encouraging results are observed. Numerical simulation results reveal the effectiveness and superiority of the proposed algorithm. In the cases of the reconstructed objects considered in this paper, the reconstructed results by the proposed algorithm show great improvement in the spatial resolution and accuracy. The spatial resolution of the reconstructed images is enhanced, and the artifacts in the reconstructed images can be removed effectively. Furthermore, the reconstructed results by the proposed algorithm under the noise-contaminated capacitance data reveal that the proposed algorithm is very competent to deal with the inaccurate nature in the capacitance data. Consequently, a promising algorithm is introduced for ECT image reconstruction.     

双正则化参数法超分辨率重建核磁共振图像

针对基于稀疏编码的超分辨率算法噪点、伪影较多的问题,提出一种双正则化参数核磁共振图像超分算法。该算法引入在线字典学习方法,以训练正则化参数λt分开训练生成精确的超完备字典对,并调整重建正则化参数λr,得到最佳的稀疏系数用于恢复目标高分图像。实验结果表明:改进算法比双字典学习超分法的目标图像峰值信噪比和结构相似性平均值分别提高了1.30 d B和0.023,有效地抑制了噪点和边缘伪影,较大幅度地提升了核磁共振图像的超分效果。     

高分辨针孔SPECT三维图像重建的实现

采用一种新颖的查找表法来实施有序子集期望值最大化（OSEM）的针孔SPECT图像重建算法,有效地将针孔响应修正包含在查找表中,进而实现高分辨针孔SPECT的三维图像重建。标准Jaszczak模具的成像实验结果表明：该方法不但能显著减少图像重建过程的计算时间和内存占用,且能显著改善重建图像的分辨率。因此,查找表法是能够快速实现针孔SPECTOSEM图像重建算法,并能将针孔响应修正包含在查找表中以获取高分辨断层图像的有效方法。     

A fully three-dimensional reconstruction algorithm with thenonstationary filter for improved single-orbit cone beam SPECT

Conventional single-orbit cone beam tomography suffers from incomplete sampling and an inadequate three-dimensional (3D) reconstruction algorithm. The commonly used Feldkamp reconstruction algorithm simply extends the two-dimensional (2D) fan beam algorithm to 3D cone beam geometry. A truly 3D reconstruction formulation based on the 3D Fourier slice theorem is derived for a single-orbit cone beam SPECT. In the formulation, a nonstationary filter which depends on the distance from the central plane of the cone beam is derived and applied to the 2D projection data in directions along and normal to the axis of rotation. This algorithm was evaluated using both computer simulation and experimental measurements. Significant improvement in image quality was demonstrated in terms of decreased artifacts and distortions in cone beam reconstructed images. However, compared with the Feldkamp algorithm, a fivefold increase in processing time is required     

基于γ射线多相流成像系统图像重建算法

在分析传统反投影图像重建产生伪迹的原因后，并考虑工业多相流特点，提出了一种基于反投影数据“求交”运算的新型射线反投影图像重建算法，新的图像重建算法可得到理想的系统点扩展函数，可较好克服重建图像伪迹。通过对典型流型仿真，证明该方法是有效的。     

基于Chambolle-Pock算法的TV重建方法研究

为实现CT稀疏视角下的投影图像重建,Sidky等设计了基于Chambolle-Pock(CP)算法,论文在此基础上实现了CP算法。仿真实验表明,与传统的滤波反投影算法相比,CP算法不存在伪影,在含噪情况下,CP算法具有较好的性能,可以实现稀疏角度下的高精度图像重建。同时,探讨了平衡因子的选取对重建精度的影响。