自适应图像全变差约束的有限角度CT重建算法

针对有限投影角度的CT图像重建问题,提出一种改进的基于自适应图像全变差（Total p Variation, TpV）约束的代数迭代重建算法。改进算法采用两相式重建结构,首先利用代数重建技术（ART）算法重建中间图像并做非负修正,然后利用自适应TpV正则项约束图像稀疏特性,进一步优化重建结果,其中正则项可根据图像区域特性自适应的调整决定平滑强度的参数p,两项交替进行直到满足收敛要求。本文应用经典的Shepp-Logan体模对改进算法进行仿真重建,以重建图像及其局部放大图作为主观分析依据,以profile图和归一化绝对距离值作为客观评估标准,与经典的ART-TV算法进行比较,对比分析重建结果发现:本文算法重建图像不仅与真实体模更接近,重建误差更小,而且能更好地保护图像的边缘特性。     

基于双层字典学习的低剂量CT图像重建算法

目的低剂量投影条件下的CT图像重建。方法采用双层K-奇异值分解(K-singular value decomposition,K-SVD)字典训练的学习方法进行图像的超分辨率重建。字典学习方法中采用KSVD算法,稀疏编码采用正交匹配追踪(orthogonal matching pursuit,OMP)算法。该算法首先利用训练库进行第一层字典训练,然后利用第一层训练的字典对低分辨率图像进行重建。进而将重建图像作为第二层待重建图像的输入,这样使得第二层输入图像含有较多的高频细节信息,因此能在重构的过程中恢复更多的细节信息,让高分辨率重构图像达到较好的效果。结果双层字典重建效果明显优于KSVD算法,重建图像更接近于原始高分辨率CT图像。结论本研究对双层字典训练学习的框架进行反迭代投影的全局优化改进,改善了图像的重建质量。     

基于选择性全变差约束的稀疏角度CT快速迭代重建算法

针对利用稀疏角度投影数据实现优质CT图像重建的问题,提出了一种改进的基于选择性图像全变差(TV)约束的快速迭代重建算法。该算法采用两相式重建策略,首先利用代数重建算法(ART)重建中间图像并进行非负性约束,然后采用选择性TV最小化对上述图像进行优化修正,两步交替进行直到满足某一收敛准则。为了进一步提升算法效能,该算法在迭代过程中应用快速收敛技术加快算法收敛。应用该算法对仿真的Sheep-Logan体模进行重建,实验结果表明,该算法不仅提高了图像的重建质量,保护了图像的边缘信息,而且显著加快了迭代重建的收敛速度。     

基于统计迭代投影估计的低剂量CT重建方法

本研究在投影域（sinogram space）建立统计模型,采用不同于传统泊松模型的信号相关高斯噪声模型,迭代实现最小化能量函数,得到理想的投影估计值后,再用滤波反投影（FBP）快速实现Radon反变换。模拟实验的结果表明,该方法有效地抑制了噪声并保持了一定的分辨率。     

CT快速图像重建算法研究

快速图像重建算法一直是图像重建中的关键问题和衡量CT系统的重要指标之一。本文以扇形束结构为例，分析了各种快速重建算法的特点，并从算法结构、实现技巧及代码优化等方面论述了快速图像重建的方法．这些方法可有效地提高图像重建的速度。     

基于全卷积神经网络的低剂量CT去噪算法

针对低剂量医学CT图像因减少辐射剂量而引入大量噪声,导致图像质量显著下降的问题,提出一种基于残差注意力机制和自适应特征融合的低剂量CT图像去噪算法,该算法使用全卷积神经网络来完成低剂量CT图像去噪。在网络框架中引入残差注意力机制和选择性内核特征融合模块,以过滤噪声信息,提取有效特征并自适应地融合图像特征,避免重建过程中的细节损失,提高图像质量,使去噪后的图像在感知上更接近原始图像。定性和定量实验表明,与现有的算法相比,在真实的临床数据集上,所提出的算法能够有效地抑制噪声,并恢复低剂量CT图像中更详细的纹理。与低剂量CT图像相比,所提出的算法将峰值信噪比提高14.94%,结构相似度提高4.68%,均方根误差降低40.11%,可以满足医学成像的诊断要求。     

口腔全景锥形束CT图像重建算法

在利用口腔锥形束CT的三维图像数据自动重建全景图时,如果锥形束CT图像中病人上、下颌骨的咬合平面不能保持水平,已有的算法将不能重建口腔全景图。为解决这一问题,本文提出一种新的全自动方法。仿照传统口腔X线全景机的成像机制,首先,在沿冠状轴的最大密度投影图像中计算出偏差角度,再旋转三维数据场;然后,在沿垂直轴的最大密度投影图像上分割牙弓区域,根据该牙弓区域就能拟合出重建全景图所需的牙弓线;最后,离散化牙弓线并沿垂直轴扩展,得到离散化的牙弓曲面,再采样合成全景图。实验结果表明本文方法较好地解决了因上、下颌骨的咬合平面不能保持水平而引起的几何畸变,从而很好地重建出口腔全景图。     

基于预扫描正则化与稀疏约束重建的低剂量CT灌注成像

CT灌注成像中患者会受到长时间的X线照射,在灌注前预先扫描一幅正常剂量图像,在后续灌注过程中进行低剂量采集,将所获低剂量图像与参考图像做减影并进行滤波处理以获得灌注信息,然后叠加到正常剂量图像中,可以非常显著地降低CT灌注成像中辐射剂量,然而,当剂量非常低的时候,重建图像会受到噪声与伪影干扰。本文基于类似的预扫描正则化数据采集方案,分别进行正常剂量和低剂量预扫描,然后利用相同的低剂量进行后续灌注过程的扫描,将所采集低剂量数据与预扫描的低剂量数据在投影域作差,然后在重建中引入稀疏性约束,以获得更准确的灌注信息重建,重建后的灌注信息最后同样叠加到正常剂量图像中。本文采用一套人脑CT灌注图像进行模拟实验,结果表明在同样剂量下,本文所提新方法重建结果所包含的灌注信息更准确,时间衰减曲线与正常剂量情况的吻合度更高,而且平均过渡时间可重复性好。     

自适应迭代重建技术在儿童胸部低剂量CT扫描中的应用价值

目的比较应用自适应迭代重建(ASi R)技术进行儿童胸部CT扫描与传统的滤过反投影法(FBP)重建在图像质量、噪声和辐射剂量方面的差别,评价ASi R技术在儿童胸部低剂量CT扫描中的应用价值。方法选择2015年8月至10月于首都儿科研究所附属儿童医院进行胸部CT检查病例60例,随机分成A、B两组,每组30例。A组年龄1个月~6岁,平均年龄2.32岁。B组年龄2个月~5岁,平均年龄2.41岁。A组采用ASi R技术进行扫描,ASi R权重值0%~50%由设备在扫描过程中自动获得。B组采用传统的FBP进行数据重建。测量所有病例左心室最大层面及同层面、同面积背部肌肉的客观噪声值,并记录容积CT剂量指数(CTDIvol)和剂量长度乘积(DLP)。2组图像均由2名高年资儿科影像医师采用4分制方法主观评价图像质量,所得数据利用t检验和Wilcoxon秩和检验做统计学分析。结果 A组病例中ASi R权重为10%2例(6.7%),20%7例(23.3%),30%10例(33.3%),40%6例(20%),50%5例(16.7%)。A组客观噪声值为23.71±4.72,B组为24.62±5.36,两组间差异无统计学意义。图像质量主观评分,2名医师的相关性较好(k=0.80),A组评分均值为3.50±0.73,B组评分均值为3.60±0.62,两组间差异无统计学意义(P0.05)。A组CTDIvol为(0.61±0.06)m Gy,B组为(1.08±0.91)m Gy;与B组相比,A组辐射剂量平均降低了44.6%,最大降幅为59.3%,两组间差异有显著统计学意义(P0.001)。结论儿童胸部CT扫描中,应用ASi R技术在保证图像质量、满足临床诊断要求的前提下,可降低40%以上的辐射剂量。     

基于压缩感知的CT重建算法的研究现状

压缩感知理论是一种新兴的信号获取与处理理论,通过减少信号重建所需的数据以缩短信号采样时间,减少计算量,并在一定程度上保持原有图像的重建质量,由此可以解决在CT重建中还普遍存在的清晰度不够高、线性度不够好和有噪声伪影干扰等问题。由于该理论的这些显著优点,使其在CT成像领域引起了广泛关注,取得了很大进展。本文对近几年压缩感知应用于CT重建的研究方法和成果进行归纳和分析,其中包括传统统计迭代算法与压缩感知理论相结合方法的分析,先验图像约束与压缩感知理论相结合方法的分析以及字典学习的发展历程分析。最后,对该研究领域的发展进行了展望。     

Low-dose CT reconstruction via edge-preserving total variation regularization

High radiation dose in computed tomography (CT) scans increases the lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with total variation (TV) regularization have been developed to reconstruct CT images from highly undersampled data acquired at low mAs levels in order to reduce the imaging dose. Nonetheless, the low-contrast structures tend to be smoothed out by the TV regularization, posing a great challenge for the TV method. To solve this problem, in this work we develop an iterative CT reconstruction algorithm with edge-preserving TV (EPTV) regularization to reconstruct CT images from highly undersampled data obtained at low mAs levels. The CT image is reconstructed by minimizing energy consisting of an EPTV norm and a data fidelity term posed by the x-ray projections. The EPTV term is proposed to preferentially perform smoothing only on the non-edge part of the image in order to better preserve the edges, which is realized by introducing a penalty weight to the original TV norm. During the reconstruction process, the pixels at the edges would be gradually identified and given low penalty weight. Our iterative algorithm is implemented on graphics processing unit to improve its speed. We test our reconstruction algorithm on a digital NURBS-based cardiac-troso phantom, a physical chest phantom and a Catphan phantom. Reconstruction results from a conventional filtered backprojection (FBP) algorithm and a TV regularization method without edge-preserving penalty are also presented for comparison purposes. The experimental results illustrate that both the TV-based algorithm and our EPTV algorithm outperform the conventional FBP algorithm in suppressing the streaking artifacts and image noise under a low-dose context. Our edge-preserving algorithm is superior to the TV-based algorithm in that it can preserve more information of low-contrast structures and therefore maintain acceptable spatial resolution.     

基于全变分模型的CT不完全角度重建算法研究进展

在计算机断层扫描成像领域,不完全角度重建算法可以在不完备的投影数据中重建出质量较好的图像,而其中比较突出的一类算法是基于全变分模型的重建算法。研究者们在此模型的基础上提出了许多相关的算法,重建出了质量更好的图像。本文首先简要介绍了全变分模型重建算法,然后在模型改进和求解算法两个方面对此模型的重建算法进行研究。在模型改进方面主要介绍了根据全变分模型的局限性以及图像的内涵信息引入相关的先验（方向信息、非局部信息、高阶梯度信息等）来改善图像的重建性能。在求解算法方面主要介绍了经典的梯度下降算法以及基于稀疏优化理论的交替方向最小化算法。最后分析总结了目前存在的问题以及提出模型改进和求解算法两方面相结合依旧是未来发展的趋势。     

Evaluation of robustness of maximum likelihood cone-beam CT reconstruction with total variation regularization

The objective of this paper is to evaluate an iterative maximum likelihood (ML) cone-beam computed tomography (CBCT) reconstruction with total variation (TV) regularization with respect to the robustness of the algorithm due to data inconsistencies. Three different and (for clinical application) typical classes of errors are considered for simulated phantom and measured projection data: quantum noise, defect detector pixels and projection matrix errors. To quantify those errors we apply error measures like mean square error, signal-to-noise ratio, contrast-to-noise ratio and streak indicator. These measures are derived from linear signal theory and generalized and applied for nonlinear signal reconstruction. For quality check, we focus on resolution and CT-number linearity based on a Catphan phantom. All comparisons are made versus the clinical standard, the filtered backprojection algorithm (FBP). In our results, we confirm and substantially extend previous results on iterative reconstruction such as massive undersampling of the number of projections. Errors of projection matrix parameters of up to 1° projection angle deviations are still in the tolerance level. Single defect pixels exhibit ring artifacts for each method. However using defect pixel compensation, allows up to 40% of defect pixels for passing the standard clinical quality check. Further, the iterative algorithm is extraordinarily robust in the low photon regime (down to 0.05 mAs) when compared to FPB, allowing for extremely low-dose image acquisitions, a substantial issue when considering daily CBCT imaging for position correction in radiotherapy. We conclude that the ML method studied herein is robust under clinical quality assurance conditions. Consequently, low-dose regime imaging, especially for daily patient localization in radiation therapy is possible without change of the current hardware of the imaging system.     

Higher order total variation regularization for EIT reconstruction

Electrical impedance tomography (EIT) attempts to reveal the conductivity distribution of a domain based on the electrical boundary condition. This is an ill-posed inverse problem; its solution is very unstable. Total variation (TV) regularization is one of the techniques commonly employed to stabilize reconstructions. However, it is well known that TV regularization induces staircase effects, which are not realistic in clinical applications. To reduce such artifacts, modified TV regularization terms considering a higher order differential operator were developed in several previous studies. One of them is called total generalized variation (TGV) regularization. TGV regularization has been successively applied in image processing in a regular grid context. In this study, we adapted TGV regularization to the finite element model (FEM) framework for EIT reconstruction. Reconstructions using simulation and clinical data were performed. First results indicate that, in comparison to TV regularization, TGV regularization promotes more realistic images.

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Graphical abstract Reconstructed conductivity changes located on selected vertical lines. For each of the reconstructed images as well as the ground truth image, conductivity changes located along the selected left and right vertical lines are plotted. In these plots, the notation GT in the legend stands for ground truth, TV stands for total variation method, and TGV stands for total generalized variation method. Reconstructed conductivity distributions from the GREIT algorithm are also demonstrated.

     

Weighted FBP--a simple approximate 3D FBP algorithm for multislice spiral CT with good dose usage for arbitrary pitch

A new 3D reconstruction scheme, weighted filtered backprojection (WFBP) for multirow spiral CT based on an extension of the two-dimensional SMPR algorithm is described and results are presented. In contrast to other 3D algorithms available, the algorithm makes use of all available data for all pitch values. The algorithm is a FBP algorithm: linear convolution of the parallel data along the row direction followed by a 3D backprojection. Data usage for arbitrary pitch values is maintained through a weighting scheme which takes into account redundant data. If proper row weighting is applied, the image quality is superior to the image quality of the SMPR algorithm.     

A combination-weighted Feldkamp-based reconstruction algorithm for cone-beam CT

The combination-weighted Feldkamp algorithm (CW-FDK) was developed and tested in a phantom in order to reduce cone-beam artefacts and enhance cranio-caudal reconstruction coverage in an attempt to improve image quality when utilizing cone-beam computed tomography (CBCT). Using a 256-slice cone-beam CT (256CBCT), image quality (CT-number uniformity and geometrical accuracy) was quantitatively evaluated in phantom and clinical studies, and the results were compared to those obtained with the original Feldkamp algorithm. A clinical study was done in lung cancer patients under breath holding and free breathing. Image quality for the original Feldkamp algorithm is degraded at the edge of the scan region due to the missing volume, commensurate with the cranio-caudal distance between the reconstruction and central planes. The CW-FDK extended the reconstruction coverage to equal the scan coverage and improved reconstruction accuracy, unaffected by the cranio-caudal distance. The extended reconstruction coverage with good image quality provided by the CW-FDK will be clinically investigated for improving diagnostic and radiotherapy applications. In addition, this algorithm can also be adapted for use in relatively wide cone-angle CBCT such as with a flat-panel detector CBCT.     

Nonparametric optimization of constrained total variation for tomography reconstruction

Iterative algorithms based on constrained total-variation (TV) optimization are effective for the reconstruction of limited data from X-ray computed tomography (CT). Such algorithms can be executed by implementing alternative operations projection onto convex sets (POCS) on the constraints, and a gradient descent approach for TV objective minimization. To balance TV-gradient descent with POCS, the adaptive-steepest-descent (ASD) method utilizes a set of complicated parameters to adjust the TV-gradient-descent step-size. The optimal parameters are difficult for users to select, and moreover, users have to empirically choose different parameters when reconstructing different types of images. To deal with these drawbacks, this paper proposes a nonparametric method for constrained TV optimization. The method automatically updates the step-size of TV iteration according to the changes in the consistency term defined by the constraints without introducing artificial parameters. The proposed method avoids the time-consuming parameter optimization, and can be conveniently implemented in various applications. Experimental results on phantom data demonstrate the flexibility and effectiveness of the proposed method.     

A three-dimensional reconstruction algorithm for an inverse-geometry volumetric CT system

An inverse-geometry volumetric computed tomography (IGCT) system has been proposed capable of rapidly acquiring sufficient data to reconstruct a thick volume in one circular scan. The system uses a large-area scanned source opposite a smaller detector. The source and detector have the same extent in the axial, or slice, direction, thus providing sufficient volumetric sampling and avoiding cone-beam artifacts. This paper describes a reconstruction algorithm for the IGCT system. The algorithm first rebins the acquired data into two-dimensional (2D) parallel-ray projections at multiple tilt and azimuthal angles, followed by a 3D filtered backprojection. The rebinning step is performed by gridding the data onto a Cartesian grid in a 4D projection space. We present a new method for correcting the gridding error caused by the finite and asymmetric sampling in the neighborhood of each output grid point in the projection space. The reconstruction algorithm was implemented and tested on simulated IGCT data. Results show that the gridding correction reduces the gridding errors to below one Hounsfield unit. With this correction, the reconstruction algorithm does not introduce significant artifacts or blurring when compared to images reconstructed from simulated 2D parallel-ray projections. We also present an investigation of the noise behavior of the method which verifies that the proposed reconstruction algorithm utilizes cross-plane rays as efficiently as in-plane rays and can provide noise comparable to an in-plane parallel-ray geometry for the same number of photons. Simulations of a resolution test pattern and the modulation transfer function demonstrate that the IGCT system, using the proposed algorithm, is capable of 0.4 mm isotropic resolution. The successful implementation of the reconstruction algorithm is an important step in establishing feasibility of the IGCT system.