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.

     

低剂量CT的加权总变差重建算法

针对稀疏投影角度的CT图像重建问题,结合压缩感知理论,提出基于加权迭代支持检测的分块代数重建算法,以较少的投影角度重建出理想的CT图像。首先,针对传统的代数重建技术计算量大、收敛速度慢的问题,提出分块代数重建算法;其次,传统的最小总变差模型会引起图像过度平滑及纹理细节模糊等问题,对此提出一种最小加权总变差算法,即加权迭代支持检测算法,并建立加权迭代支持检测模型;最后,分块代数重建技术与加权迭代支持检测模型交替迭代,使重建结果趋于收敛。本文采用经典的Shepp-Logan体模及实际的脑部CT切片进行重建,以均方根误差作为重建图像的质量评判标准,并与其他重建算法的重建结果进行对比。在经过一定次数的迭代后,基于本文算法的重建图像更贴近原始图像,而且比其他算法更早收敛。实验结果表明,本文算法在重建质量及收敛速度上都优于其他对比算法。     

GPU-based iterative cone-beam CT reconstruction using tight frame regularization

The x-ray imaging dose from serial cone-beam computed tomography (CBCT) scans raises a clinical concern in most image-guided radiation therapy procedures. It is the goal of this paper to develop a fast graphic processing unit (GPU)-based algorithm to reconstruct high-quality CBCT images from undersampled and noisy projection data so as to lower the imaging dose. For this purpose, we have developed an iterative tight-frame (TF)-based CBCT reconstruction algorithm. A condition that a real CBCT image has a sparse representation under a TF basis is imposed in the iteration process as regularization to the solution. To speed up the computation, a multi-grid method is employed. Our GPU implementation has achieved high computational efficiency and a CBCT image of resolution 512 × 512 × 70 can be reconstructed in ～5 min. We have tested our algorithm on a digital NCAT phantom and a physical Catphan phantom. It is found that our TF-based algorithm is able to reconstruct CBCT in the context of undersampling and low mAs levels. We have also quantitatively analyzed the reconstructed CBCT image quality in terms of the modulation-transfer function and contrast-to-noise ratio under various scanning conditions. The results confirm the high CBCT image quality obtained from our TF algorithm. Moreover, our algorithm has also been validated in a real clinical context using a head-and-neck patient case. Comparisons of the developed TF algorithm and the current state-of-the-art TV algorithm have also been made in various cases studied in terms of reconstructed image quality and computation efficiency.     

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。     

Joint L1 and total variation regularization for fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is an imaging modality that exploits the specificity of fluorescent biomarkers to enable 3D visualization of molecular targets and pathways in vivo in small animals. Owing to the high degree of absorption and scattering of light through tissue, the FMT inverse problem is inherently ill-conditioned making image reconstruction highly susceptible to the effects of noise and numerical errors. Appropriate priors or penalties are needed to facilitate reconstruction and to restrict the search space to a specific solution set. Typically, fluorescent probes are locally concentrated within specific areas of interest (e.g., inside tumors). The commonly used L(2) norm penalty generates the minimum energy solution, which tends to be spread out in space. Instead, we present here an approach involving a combination of the L(1) and total variation norm penalties, the former to suppress spurious background signals and enforce sparsity and the latter to preserve local smoothness and piecewise constancy in the reconstructed images. We have developed a surrogate-based optimization method for minimizing the joint penalties. The method was validated using both simulated and experimental data obtained from a mouse-shaped phantom mimicking tissue optical properties and containing two embedded fluorescent sources. Fluorescence data were collected using a 3D FMT setup that uses an EMCCD camera for image acquisition and a conical mirror for full-surface viewing. A range of performance metrics was utilized to evaluate our simulation results and to compare our method with the L(1), L(2) and total variation norm penalty-based approaches. The experimental results were assessed using the Dice similarity coefficients computed after co-registration with a CT image of the phantom.     

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.     

CT三维重建在全膝关节置换中的应用

背景：下肢X射线测量及CT三维重建的应用,以及计算机辅助技术都有助于人工全膝关节置换术者更精确地安放假体。 目的：探讨全膝关节置换前CT三维重建确定股骨髓内定位杆置入点对置换后关节功能的影响。 方法：32例全膝关节置换患者,其中置换前进行CT三维重建确定股骨髓内定位杆置入点的18个病例(CT三维重建组),其余病例术前未进行CT三维重建(对照组),在置换后3个月、1年、2年定期随访。 结果与结论：置换后3个月、1年、2年随访与对照组比较,CT三维重建组膝关节功能评分总体功能和单纯膝关节功能评分显著增高(P均 < 0.05)。提示全膝关节置换前行膝关节CT三维重建确定股骨髓内定位杆进入点有助于在置换中正确插入股骨髓内定位杆,更准确地进行股骨端的截骨以及膝关节假体的安放,能够更好地恢复下肢力线和膝关节的功能。     

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。     

Improved total variation-based CT image reconstruction applied to clinical data

In computed tomography there are different situations where reconstruction has to be performed with limited raw data. In the past few years it has been shown that algorithms which are based on compressed sensing theory are able to handle incomplete datasets quite well. As a cost function these algorithms use the ?(1)-norm of the image after it has been transformed by a sparsifying transformation. This yields to an inequality-constrained convex optimization problem. Due to the large size of the optimization problem some heuristic optimization algorithms have been proposed in the past few years. The most popular way is optimizing the raw data and sparsity cost functions separately in an alternating manner. In this paper we will follow this strategy and present a new method to adapt these optimization steps. Compared to existing methods which perform similarly, the proposed method needs no a priori knowledge about the raw data consistency. It is ensured that the algorithm converges to the lowest possible value of the raw data cost function, while holding the sparsity constraint at a low value. This is achieved by transferring the step-size determination of both optimization procedures into the raw data domain, where they are adapted to each other. To evaluate the algorithm, we process measured clinical datasets. To cover a wide field of possible applications, we focus on the problems of angular undersampling, data lost due to metal implants, limited view angle tomography and interior tomography. In all cases the presented method reaches convergence within less than 25 iteration steps, while using a constant set of algorithm control parameters. The image artifacts caused by incomplete raw data are mostly removed without introducing new effects like staircasing. All scenarios are compared to an existing implementation of the ASD-POCS algorithm, which realizes the step-size adaption in a different way. Additional prior information as proposed by the PICCS algorithm can be incorporated easily into the optimization process.     

EIT image reconstruction with four dimensional regularization

Electrical impedance tomography (EIT) reconstructs internal impedance images of the body from electrical measurements on body surface. The temporal resolution of EIT data can be very high, although the spatial resolution of the images is relatively low. Most EIT reconstruction algorithms calculate images from data frames independently, although data are actually highly correlated especially in high speed EIT systems. This paper proposes a 4-D EIT image reconstruction for functional EIT. The new approach is developed to directly use prior models of the temporal correlations among images and 3-D spatial correlations among image elements. A fast algorithm is also developed to reconstruct the regularized images. Image reconstruction is posed in terms of an augmented image and measurement vector which are concatenated from a specific number of previous and future frames. The reconstruction is then based on an augmented regularization matrix which reflects the a priori constraints on temporal and 3-D spatial correlations of image elements. A temporal factor reflecting the relative strength of the image correlation is objectively calculated from measurement data. Results show that image reconstruction models which account for inter-element correlations, in both space and time, show improved resolution and noise performance, in comparison to simpler image models.     

基于深度学习的低剂量CT图像去噪

目的:提出一种基于深度学习的方法用于低剂量CT（LDCT）图像的噪声去除。方法:首先进行滤波反投影重建,然后利用多尺度并行残差U-net（MPR U-net）的深度学习模型对重建后的LDCT图像进行去噪。实验数据采用LoDoPaB-CT挑战赛的医学CT数据集,其中训练集35 820张图像,验证集3 522张图像,测试集3 553张图像,并采用峰值信噪比（PSNR）与结构相似性系数（SSIM）来评估模型的去噪效果。结果:LDCT图像处理前后PSNR分别为28.80、38.22 dB,SSIM分别为0.786、0.966,平均处理时间为0.03 s。结论:MPR U-net深度学习模型能较好地去除LDCT图像噪声,提升PSNR,保留更多图像细节。     

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。     

Fast quantitative susceptibility reconstruction via total field inversion with improved weighted L0 norm approximation

Quantitative susceptibility mapping (QSM) is a meaningful MRI technique owing to its unique relation to actual physical tissue magnetic properties. The reconstruction of QSM is usually decomposed into three sub‐problems, which are solved independently. However, this decomposition does not conform to the causes of the problems, and may cause discontinuity of parameters and error accumulation. In this paper, a fast reconstruction method named fast TFI based on total field inversion was proposed. It can accelerate the total field inversion by using a specially selected preconditioner and advanced solution of the weighted L₀ regularization. Due to the employment of an effective model, the proposed method can efficiently reconstruct the QSM of brains with lesions, where other methods may encounter problems. Experimental results from simulation and in vivo data verified that the new method has better reconstruction accuracy, faster convergence ability and excellent robustness, which may promote clinical application of QSM.