Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

Total generalized variation (TGV)-based computed tomography (CT) image reconstruction, which utilizes high-order image derivatives, is superior to total variation-based methods in terms of the preservation of edge information and the suppression of unfavorable staircase effects. However, conventional TGV regularization employs l₁-based form, which is not the most direct method for maximizing sparsity prior. In this study, we propose a total generalized p-variation (TGpV) regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems. To solve the nonconvex optimization problem of the TGpV minimization model, we then present an efficient iterative algorithm based on the alternating minimization of augmented Lagrangian function. All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying alternating minimization method and generalized p-shrinkage mapping. In addition, approximate solutions that can be easily performed and quickly calculated through fast Fourier transform are derived using the proximal point method to reduce the cost of inner subproblems. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to validate the efficiency and feasibility of the proposed method. Overall, the proposed method exhibits reasonable performance and outperforms the original TGV-based method when applied to few-view problems.     

The Impact of Iterative Reconstruction on Computed Tomography Radiation Dosimetry: Evaluation in a Routine Clinical Setting

Purpose

To evaluate the effect of introduction of iterative reconstruction as a mandated software upgrade on radiation dosimetry in routine clinical practice over a range of computed tomography examinations.

Methods

Random samples of scanning data were extracted from a centralised Picture Archiving Communication System pertaining to 10 commonly performed computed tomography examination types undertaken at two hospitals in Western Australia, before and after the introduction of iterative reconstruction. Changes in the mean dose length product and effective dose were evaluated along with estimations of associated changes to annual cancer incidence.

Results

We observed statistically significant reductions in the effective radiation dose for head computed tomography (22–27%) consistent with those reported in the literature. In contrast the reductions observed for non-contrast chest (37–47%); chest pulmonary embolism study (28%), chest/abdominal/pelvic study (16%) and thoracic spine (39%) computed tomography. Statistically significant reductions in radiation dose were not identified in angiographic computed tomography. Dose reductions translated to substantial lowering of the lifetime attributable risk, especially for younger females, and estimated numbers of incident cancers.

Conclusion

Reduction of CT dose is a priority Iterative reconstruction algorithms have the potential to significantly assist with dose reduction across a range of protocols. However, this reduction in dose is achieved via reductions in image noise. Fully realising the potential dose reduction of iterative reconstruction requires the adjustment of image factors and forgoing the noise reduction potential of the iterative algorithm. Our study has demonstrated a reduction in radiation dose for some scanning protocols, but not to the extent experimental studies had previously shown or in all protocols expected, raising questions about the extent to which iterative reconstruction achieves dose reduction in real world clinical practice.     

System Matrix Analysis for Computed Tomography Imaging

In practical applications of computed tomography imaging (CT), it is often the case that the set of projection data is incomplete owing to the physical conditions of the data acquisition process. On the other hand, the high radiation dose imposed on patients is also undesired. These issues demand that high quality CT images can be reconstructed from limited projection data. For this reason, iterative methods of image reconstruction have become a topic of increased research interest. Several algorithms have been proposed for few-view CT. We consider that the accurate solution of the reconstruction problem also depends on the system matrix that simulates the scanning process. In this work, we analyze the application of the Siddon method to generate elements of the matrix and we present results based on real projection data.     

An Efficient Augmented Lagrangian Method for Statistical X-Ray CT Image Reconstruction

Statistical iterative reconstruction (SIR) for X-ray computed tomography (CT) under the penalized weighted least-squares criteria can yield significant gains over conventional analytical reconstruction from the noisy measurement. However, due to the nonlinear expression of the objective function, most exiting algorithms related to the SIR unavoidably suffer from heavy computation load and slow convergence rate, especially when an edge-preserving or sparsity-based penalty or regularization is incorporated. In this work, to address abovementioned issues of the general algorithms related to the SIR, we propose an adaptive nonmonotone alternating direction algorithm in the framework of augmented Lagrangian multiplier method, which is termed as “ALM-ANAD”. The algorithm effectively combines an alternating direction technique with an adaptive nonmonotone line search to minimize the augmented Lagrangian function at each iteration. To evaluate the present ALM-ANAD algorithm, both qualitative and quantitative studies were conducted by using digital and physical phantoms. Experimental results show that the present ALM-ANAD algorithm can achieve noticeable gains over the classical nonlinear conjugate gradient algorithm and state-of-the-art split Bregman algorithm in terms of noise reduction, contrast-to-noise ratio, convergence rate, and universal quality index metrics.     

Micro-CT of rodents: State-of-the-art and future perspectives

Micron-scale computed tomography (micro-CT) is an essential tool for phenotyping and for elucidating diseases and their therapies. This work is focused on preclinical micro-CT imaging, reviewing relevant principles, technologies, and applications. Commonly, micro-CT provides high-resolution anatomic information, either on its own or in conjunction with lower-resolution functional imaging modalities such as positron emission tomography (PET) and single-photon emission computed tomography (SPECT). More recently, however, advanced applications of micro-CT produce functional information by translating clinical applications to model systems (e.g. measuring cardiac functional metrics) and by pioneering new ones (e.g. measuring tumor vascular permeability with nanoparticle contrast agents). The primary limitations of micro-CT imaging are the associated radiation dose and relatively poor soft tissue contrast. We review several image reconstruction strategies based on iterative, statistical, and gradient sparsity regularization, demonstrating that high image quality is achievable with low radiation dose given ever more powerful computational resources. We also review two contrast mechanisms under intense development. The first is spectral contrast for quantitative material discrimination in combination with passive or actively targeted nanoparticle contrast agents. The second is phase contrast which measures refraction in biological tissues for improved contrast and potentially reduced radiation dose relative to standard absorption imaging. These technological advancements promise to develop micro-CT into a commonplace, functional and even molecular imaging modality.     

Reduction of Metal Artifact in Single Photon-Counting Computed Tomography by Spectral-Driven Iterative Reconstruction Technique

PurposeThe exciting prospect of Spectral CT (SCT) using photon-counting detectors (PCD) will lead to new techniques in computed tomography (CT) that take advantage of the additional spectral information provided. We introduce a method to reduce metal artifact in X-ray tomography by incorporating knowledge obtained from SCT into a statistical iterative reconstruction scheme. We call our method Spectral-driven Iterative Reconstruction (SPIR).MethodThe proposed algorithm consists of two main components: material decomposition and penalized maximum likelihood iterative reconstruction. In this study, the spectral data acquisitions with an energy-resolving PCD were simulated using a Monte-Carlo simulator based on EGSnrc C++ class library. A jaw phantom with a dental implant made of gold was used as an object in this study. A total of three dental implant shapes were simulated separately to test the influence of prior knowledge on the overall performance of the algorithm. The generated projection data was first decomposed into three basis functions: photoelectric absorption, Compton scattering and attenuation of gold. A pseudo-monochromatic sinogram was calculated and used as input in the reconstruction, while the spatial information of the gold implant was used as a prior. The results from the algorithm were assessed and benchmarked with state-of-the-art reconstruction methods.ResultsDecomposition results illustrate that gold implant of any shape can be distinguished from other components of the phantom. Additionally, the result from the penalized maximum likelihood iterative reconstruction shows that artifacts are significantly reduced in SPIR reconstructed slices in comparison to other known techniques, while at the same time details around the implant are preserved. Quantitatively, the SPIR algorithm best reflects the true attenuation value in comparison to other algorithms.ConclusionIt is demonstrated that the combination of the additional information from Spectral CT and statistical reconstruction can significantly improve image quality, especially streaking artifacts caused by the presence of materials with high atomic numbers.     

Hide-and-seek strategies and post-contact immobility

To understand why an animal might gain by playing dead, or more precisely, exhibit post-contact immobility (PCI), we consider the context in which this behaviour occurs. Is it, for example, a method by which a potential victim encourages a predator to direct its attention elsewhere? We investigate this possibility by using the marginal value theorem to analyse predator behaviour in the context of this defence strategy by potential prey. We consider two models. In the first, (random revisiting) the predator may return to sites it has already depleted within the patch. In the second, (systematic search) the predator goes only to new sites within the patch. The results of the two models are qualitatively extremely similar. We show that when prey occur in patches, PCI favours prey survival. Indeed, certain antlion larvae have PCI durations characterized by very long half-lives. These appear to be of such long durations that further increases would convey no substantial benefits in redirecting potential predators to other antlions within the patch and subsequently to other patches.     

Multi-Mounted X-Ray Computed Tomography

Most existing X-ray computed tomography (CT) techniques work in single-mounted mode and need to scan the inspected objects one by one. It is time-consuming and not acceptable for the inspection in a large scale. In this paper, we report a multi-mounted CT method and its first engineering implementation. It consists of a multi-mounted scanning geometry and the corresponding algebraic iterative reconstruction algorithm. This approach permits the CT rotation scanning of multiple objects simultaneously without the increase of penetration thickness and the signal crosstalk. Compared with the conventional single-mounted methods, it has the potential to improve the imaging efficiency and suppress the artifacts from the beam hardening and the scatter. This work comprises a numerical study of the method and its experimental verification using a dataset measured with a developed multi-mounted X-ray CT prototype system. We believe that this technique is of particular interest for pushing the engineering applications of X-ray CT.     

A Novel Weighted Total Difference Based Image Reconstruction Algorithm for Few-View Computed Tomography

In practical applications of computed tomography (CT) imaging, due to the risk of high radiation dose imposed on the patients, it is desired that high quality CT images can be accurately reconstructed from limited projection data. While with limited projections, the images reconstructed often suffer severe artifacts and the edges of the objects are blurred. In recent years, the compressed sensing based reconstruction algorithm has attracted major attention for CT reconstruction from a limited number of projections. In this paper, to eliminate the streak artifacts and preserve the edge structure information of the object, we present a novel iterative reconstruction algorithm based on weighted total difference (WTD) minimization, and demonstrate the superior performance of this algorithm. The WTD measure enforces both the sparsity and the directional continuity in the gradient domain, while the conventional total difference (TD) measure simply enforces the gradient sparsity horizontally and vertically. To solve our WTD-based few-view CT reconstruction model, we use the soft-threshold filtering approach. Numerical experiments are performed to validate the efficiency and the feasibility of our algorithm. For a typical slice of FORBILD head phantom, using 40 projections in the experiments, our algorithm outperforms the TD-based algorithm with more than 60% gains in terms of the root-mean-square error (RMSE), normalized root mean square distance (NRMSD) and normalized mean absolute distance (NMAD) measures and with more than 10% gains in terms of the peak signal-to-noise ratio (PSNR) measure. While for the experiments of noisy projections, our algorithm outperforms the TD-based algorithm with more than 15% gains in terms of the RMSE, NRMSD and NMAD measures and with more than 4% gains in terms of the PSNR measure. The experimental results indicate that our algorithm achieves better performance in terms of suppressing streak artifacts and preserving the edge structure information of the object.     

3D Algebraic Iterative Reconstruction for Cone-Beam X-Ray Differential Phase-Contrast Computed Tomography

Due to the potential of compact imaging systems with magnified spatial resolution and contrast, cone-beam x-ray differential phase-contrast computed tomography (DPC-CT) has attracted significant interest. The current proposed FDK reconstruction algorithm with the Hilbert imaginary filter will induce severe cone-beam artifacts when the cone-beam angle becomes large. In this paper, we propose an algebraic iterative reconstruction (AIR) method for cone-beam DPC-CT and report its experiment results. This approach considers the reconstruction process as the optimization of a discrete representation of the object function to satisfy a system of equations that describes the cone-beam DPC-CT imaging modality. Unlike the conventional iterative algorithms for absorption-based CT, it involves the derivative operation to the forward projections of the reconstructed intermediate image to take into account the differential nature of the DPC projections. This method is based on the algebraic reconstruction technique, reconstructs the image ray by ray, and is expected to provide better derivative estimates in iterations. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a mini-focus x-ray tube source. It is shown that the proposed method can reduce the cone-beam artifacts and performs better than FDK under large cone-beam angles. This algorithm is of interest for future cone-beam DPC-CT applications.     

A dynamic habitat selection game

A patch selection game is formulated and analyzed. Organisms can forage in one of H patches. Each patch is characterized by the cost of foraging, the density and value of food, the predation risk, and the density of conspecifics. The presence of conspecifics affects the finding and sharing of food, and the predation risk. Optimal foraging theory can be viewed as a "1-person" game against nature in which the optimal patch choice of a specific organism is analyzed assuming that the number of conspecifics in other patches is fixed. In the general game theoretic approach, the behavior of conspecifics is included in the determination of the distinguished organism's strategy. An iterative algorithm is used to compute the solution of the "n-person" game or dynamic ESS, which differs from the optimal foraging theory solution. Experiments to test the proposed theory using rodents and seed trays are briefly discussed.     

高寒草甸不同扰动斑块植物功能群和根土复合体特征变化研究

高原鼠兔(Ochotonacurzoniae)活动在高寒草甸上会形成各种类型扰动斑块,扰动斑块类型的转变是导致草地退化的原因之一。目前,斑块类型发生转变的关键影响因子尚不清楚,因此,对高寒草甸活动斑块、非活动斑块和恢复斑块三个扰动斑块类型植物功能类群结构、根土复合体特征和斑块分布特征进行研究,旨在探讨斑块类型发生转变的主要因子,说明高寒草甸退化机理。研究结果表明,高寒草甸中活动斑块土壤表层由于放牧和高原鼠兔活动扰动强度大,无法形成稳定的植物群落,非活动斑块的植物群落处于次生演替早期阶段,但是恢复斑块已具备高寒草甸优势种莎草科植物生长的基本条件。退化高寒草甸中活动斑块与非活动斑块呈现镶嵌性分布,而恢复斑块相对独立没有镶嵌性分布现象。造成高寒草甸干扰斑块类型转变的主要原因是高原鼠兔活动强度由间歇性干扰转变为持续干扰的结果。     

Electron Tomography of Large, Multicomponent Biological Structures

Electron tomography is an extremely useful method for deriving three-dimensional structure from electron microscope images. The application of this technique to the reconstruction of large, complex structures such as mitochondria is described in conjunction with several tools for segmentation, measurement, classification, and visualization. In addition, the use of massively parallel computers to perform the tomographic reconstruction efficiently using R-weighted backprojection or iterative techniques is described.     

双源CT三维重建前交叉韧带移植物新技术

目的:探讨双源CT(DSCT)三维重建前交叉韧带(anterior cruciate ligament,ACL)重建术后移植物的技术方法。方法:对30例ACL损伤后移植重建术后患者进行DSCT扫描,利用软件三维重建ACL移植物的三维图像,对图像效果进行分析。结果:采用设定的参数和方法,30例患者的ACL移植物均获得三维重现,其中24例获得清晰的移植物图像,6例移植物图像略模糊。结论:DSCT可以重建出移植术后ACL移植物的三维图像,对临床检验、评估重建技术、修正重建方法、实现解剖重建有重大价值。     

ATOM 1.0:基于GPU的电子断层重构软件

电子断层成像技术能够在纳米尺度下重构出不具有全同性的细胞或大分子的三维结构,正受到越来越广泛的重视。针对现有电子断层成像技术中重构软件的不足,特别是迭代重构算法速度慢的缺点,我们开发了一款基于Graphic Processor Unit(GPU)平台的电子断层重构软件——ATOM,实现了图像对位、重构参数计算、三维重构及数据可视化等电子断层重构的基本功能。其中,在二维对位方面,ATOM实现了迭代的无标记平移和旋转对位;在三维重构方面,实现了背投影和多种迭代重构算法,并实现了迭代重构在GPU平台上的并行加速,获得了良好的加速比,如SIRT算法得到了47倍加速比。ATOM是绿色开源软件,可以运行在支持Qt和CUDA的所有操作系统上。ATOM为图形界面软件,结合详尽的安装及使用文档,便于用户使用。     

A Multiresolution Approach to Discrete Tomography Using DART

In discrete tomography, a scanned object is assumed to consist of only a few different materials. This prior knowledge can be effectively exploited by a specialized discrete reconstruction algorithm such as the Discrete Algebraic Reconstruction Technique (DART), which is capable of providing more accurate reconstructions from limited data compared to conventional reconstruction algorithms. However, like most iterative reconstruction algorithms, DART suffers from long computation times. To increase the computational efficiency as well as the reconstruction quality of DART, a multiresolution version of DART (MDART) is proposed, in which the reconstruction starts on a coarse grid with big pixel (voxel) size. The resulting reconstruction is then resampled on a finer grid and used as an initial point for a subsequent DART reconstruction. This process continues until the target pixel size is reached. Experiments show that MDART can provide a significant speed-up, reduce missing wedge artefacts and improve feature reconstruction in the object compared with DART within the same time, making its use with large datasets more feasible.     

3D TOF-PET image reconstruction using total variation regularization

In this paper we introduce a semi-analytic algorithm for 3-dimensional image reconstruction for positron emission tomography (PET). The method consists of the back-projection of the acquired data into the most likely image voxel according to time-of-flight (TOF) information, followed by the filtering step in the image space using an iterative optimization algorithm with a total variation (TV) regularization. TV regularization in image space is more computationally efficient than usual iterative optimization methods for PET reconstruction with full system matrix that use TV regularization. The efficiency comes from the one-time TOF back-projection step that might also be described as a reformatting of the acquired data. An important aspect of our work concerns the evaluation of the filter operator of the linear transform mapping an original radioactive tracer distribution into the TOF back-projected image. We obtain concise, closed-form analytical formula for the filter operator. The proposed method is validated with the Monte Carlo simulations of the NEMA IEC phantom using a one-layer, 50 cm-long cylindrical device called Jagiellonian PET scanner. The results show a better image quality compared with the reference TOF maximum likelihood expectation maximization algorithm.     

Accelerating an Ordered-Subset Low-Dose X-Ray Cone Beam Computed Tomography Image Reconstruction with a Power Factor and Total Variation Minimization

In recent years, there has been increased interest in low-dose X-ray cone beam computed tomography (CBCT) in many fields, including dentistry, guided radiotherapy and small animal imaging. Despite reducing the radiation dose, low-dose CBCT has not gained widespread acceptance in routine clinical practice. In addition to performing more evaluation studies, developing a fast and high-quality reconstruction algorithm is required. In this work, we propose an iterative reconstruction method that accelerates ordered-subsets (OS) reconstruction using a power factor. Furthermore, we combine it with the total-variation (TV) minimization method. Both simulation and phantom studies were conducted to evaluate the performance of the proposed method. Results show that the proposed method can accelerate conventional OS methods, greatly increase the convergence speed in early iterations. Moreover, applying the TV minimization to the power acceleration scheme can further improve the image quality while preserving the fast convergence rate.     

基于最小模估计及Tikhonov正则方法的脑磁源重建

脑磁图（magnetoencephalogram,MEG）研究中的磁源分布图象重建,属于不适定问题,需要引入适合的先验约束,把它转化为适定问题。采用非参数的分布源模型,磁源成象问题即为求解病态的欠定的线性方程组。这里采用的方法是建立在最小模估计和Tikhonov正则的基础上,从数学算法本身及相关的解剖学和神经生理学的信息,对解空间加以限制,提出了区域加权算子,再结合深工加权,以期得到合理的神经电流分布。通过仿真实验表明能得出理想的重建结果,同时讨论了该方法的局限性以及下一步的工作方向。     

Single-particle reconstruction using L(2)-gradient flow

In this paper, we present an iterative algorithm for reconstructing a three-dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an L²-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Our method compares favorably with those of the weighted back projection, Fourier method, algebraic reconstruction technique and simultaneous iterative reconstruction technique.