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.     

Constrained Optimization Algorithms for Divergent Ray Tomography

Using the projections as constraints, the reconstruction of an object from its fan beam projections is formulated and solved as a problem in constrained optimization. First a general cost criterion is optimized and the result is applied to several specific criteria. This produces a number of relationships (models) between the image and the Lagrange multipliers introduced by the Euler-Lagrange method. Utilizing these models, the ART methods are extended to fan beam projections. A non-recursive algorithm which exploits the speed of the block fast Fourier transform is given and compared with an existing convolution algorithm. The projection slice theorem for divergent ray geometry is given by introducing a new transform, the Angular Projection Transform.     

Tomographic Algorithms for General Line Integrals

This paper extends the constrained optimization image reconstruction techniques to curved-ray projections for a number of scanning systems and for 2-D and 3-D reconstructions. Teh treatment presented is general in that it includes the previous results on parallel-ray and divergent-ray geometries as special casss. Employing the projection data as constraints, the reconstruction problem is expressed as a generalized constrained optimization problem whose solution leads to a relationship (model) between the reconstruction and the associate Lagrange multiplier functions, thus introducting the models for a number of prescribed cost criteria and scanning systems involing curved-ray projections. Using these new models a category of subspaces of a Hirbert space, the elements of which are the functions (objects) for reconstruction, is presented. The projections and the minimum energy reconstruction are shown to be projections of the object into these new subspaces. The projection slice theorem is extended by introducing a new transform, a slice of which is equal to the Fourier series of the corresponding projection, irrespective of the projection geometry. The ART methods are extended to curved-ray scanning systems. Also a convergent iterative algorithms which evaluates the Lagrange multipliers from general line integrals and then calculates the reconstruction, is introduced. The iterations of this algorithm are identical to those of the additive ART, thus resulting in the same solution.     

基于Radon变换导数的精确三维CT图像重建理论与改进方法介绍

本文主要介绍了一种基于Ｒａｄｏｎ变换导数的精确３Ｄ－ＣＴ图像重建的改进方法，它的计算复杂性和成像质量与传统方法相比有很大改善。     

Iterative restoration of SPECT projection images

Photon attenuation and the limited nonstationary spatial resolution of the detector can reduce both qualitative and quantitative image quality in single photon emission computed tomography (SPECT). In this paper, a reconstruction approach is described which can compensate for both of these degradations. The approach involves processing the projection data with Bellini's method for attenuation compensation followed by an iterative deconvolution technique which uses the frequency distance principle (FDP) to model the distance-dependent camera blur. Modeling of the camera blur with the FDP allows an efficient implementation using fast Fourier transform (FFT) methods. After processing of the projection data, reconstruction is performed using filtered backprojection. Simulation studies using two different brain phantoms show that this approach gives reconstructions with a favorable bias versus noise tradeoff, provides no visually undesirable noise artifacts, and requires a low computational load     

基于DSP技术的工业CT重建软件设计

提出了基于现代数字信号处理器(DSP)技术进行CT重建软件设计.在实际的CT软件设计过程中,利用TI的C6701 DSP芯片的硬件处理系统,建立了基于DSP硬件系统的CT算法重建软件,该软件全部使用与DSP硬件系统相关的DSP汇编语言进行编程.并利用TI的C6701 EVM开发板,通过输入CT数据进行计算,得出的CT图像满足实际要求.     

CT图像重建方法在半影成像中的应用

CT图像重建方法和半影成像是两种传统的辐射图像诊断方式。将CT图像重建方法应用到半影图像数据处理中,探索出一种新的半影图像处理方法。在新的半影编码孔图像数据处理中,首次应用了与图像诊断系统点扩散函数无关的编码孔图像处理方法,解决了传统编码孔图像处理中由于图像诊断系统点扩散函数不确定带来的技术难题。在理论研究的基础上进行了半影模拟成像及图像重建,获得了理想的研究结果。     

由相叠的低分辨扇形束投影数据重建高分辨CT图像

在研究扇形束插值代数重建法基础上，提出了由相叠的低分辨扇形束投影数据重建高分辨CT图像的两个新算法，即扇形束的虚拟探测器法和扇形束的直接重建法，并给出和分析了数值模拟结果。     

Novel fluctuation reduction procedure for nuclear reactivity calculations based on the discrete fourier transform method

A new method for calculating nuclear reactivity based on the Discrete Fourier Transform (DFT) – with two filters: a first-order delay low-pass filter and a Savitzky-Golay filter – is presented. The reactivity is calculated from an integrodifferential equation known as the inverse point kinetic equation, which contains the history of neutron population density. The new method can be understood as a convolution between the neutron population density signal and the response to the characteristic impulse of a linear system. The proposed method is based on the discrete Fourier transform (DFT) that performs a circular convolution. The fast Fourier transform algorithm (FFT) with the zero-padding technique is implemented to reduce the computational cost.     

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.     

An investigation of two-phase flow instability using wavelet signal extraction technique

When the oscillation periods of the instability of two-phase flow are sought with traditional methods of signal analysis, generally the Fourier transform must be employed and then the oscillation periods will be gotten at the location of the local maximum amplitude of frequency transform. However, Fourier transform will be difficult to clearly analyze the unsteady signals especially when the signals include many peaks and the noise interference is not generated by white noise in many areas of practical engineering like the oscillation of the instability of two-phase flow. The most effective solving method for the difficulty of Fourier transform is to analyze the signals directly in time domain. Wavelet analysis is able to search out the periods from time domain directly. It also has more excellent local characteristics than Fourier analysis in the both of time and frequency domains. In this paper, not only is a direct detecting method of the oscillation periods successfully applied based on the wavelet signal extraction techniques, but also the oscillation of density wave type of TYPE I is found as a kind of oscillations with a high-frequency harmonization.     

锥束CT扫描方式对ART算法图像重建的影响研究

平板探测器锥束CT的扫描方式对ART(Algebraic Reconstruction Techniques)算法图像重建会产生影响.本文用128×128×128三维Shepp-Logan头部模型作为仿真对象,探讨了不同源-扫描中心距离、投影数、缺角度下扫描方式对图像重建的影响.结果表明,源-扫描中心距离与扫描中心-探...     

基于重投影的CT图像硬化伪影校正

在工业计算机断层成像(CT)技术中所用的X射线源通常是多能的,检测过程中只能获得多能投影数据,若直接重建图像则会出现硬化伪影,硬化伪影校正是提高重建图像质量的一重要步骤。本文采用重投影的方法来校正由于射线硬化导致重建图像出现的硬化伪影,通过硬化校正后的重建CT图像质量得到显著提高。     

Mathematical Aspects of NMR Tomography

Mathematical aspects of Nuclear Magnetic Resonance (NMR) tomography are discussed. Two main image formation schemes reviewed are the projection reconstruction and direct Fourier imaging techniques. Specific cases of two- and three-dimensional NMR imaging are also presented.     

集装箱CT检测系统中贝叶斯图像重建算法的应用探讨

最大后验概率(Maximum a posteriori,MAP)图像重建算法是一种贝叶斯算法(Bayesian Reconstruction,BR),可克服最大似然(Maximum Likelihood,ML)算法不能抑制噪声、重建时间较长的缺点.探讨了适合集装箱CT检测的两种MAP重建算法:加权最小二乘-最大后验概率-共轭梯度算法(weighted-least-squares MAP conjugate gradient,WLS-MAP-CG)和有序子集-贝叶斯算法(modified ordered subset,MOS-BR)并讨论了合适的先验知识分布.     

Study of R.f., Gradient Pulse and Magnet Instability Effect in NMR Tomography

Newly emerged NMR imaging requires careful studies on r. f. pulse shapes and sequencing for the selection of the region, gradient pulsing for the 2- or 3-D spatial coding, and suitable signal handling technique for the compensation of the inherent instability of the system, especially fluctuation of the static magnetic field. Above subjects are discussed in detail and a new method which would be useful for the line integral projection reconstruction is proposed. The method could equally be applied to other 3-D NMR imaging techniques such as KWE (Kumar-Welti-Ernst) direct Fourier reconstruction or planar integral projection type reconstruction.     

离散傅里叶变换在电离辐射探测器性能分析中的应用

为了研制性能优良的电离室探测器前置放大器，以满足冷轧钢板测厚仪的需要，本文将傅里叶分析方法应用于电离室探测器前置放大器的性能分析中。通过对探测器零点数据的离散傅里叶变换（DFT），对电离室探测器前置放大器的设计予以有效的指导，设计出应用于实际冷轧钢板测厚仪中的电离室探测器前置放大器。     

Slice-wise reconstruction for low-dose cone-beam CT using a deep residual convolutional neural network

Because of the growing concern over the radiation dose delivered to patients, X-ray cone-beam CT(CBCT) imaging of low dose is of great interest. It is difficult for traditional reconstruction methods such as Feldkamp to reduce noise and keep resolution at low doses. A typical method to solve this problem is using optimizationbased methods with careful modeling of physics and additional constraints. However, it is computationally expensive and very time-consuming to reach an optimal solution. Recently, some pioneering work applying deep neural networks had some success in characterizing and removing artifacts from a low-dose data set. In this study,we incorporate imaging physics for a cone-beam CT into a residual convolutional neural network and propose a new end-to-end deep learning-based method for slice-wise reconstruction. By transferring 3D projection to a 2D problem with a noise reduction property, we can not only obtain reconstructions of high image quality, but also lower the computational complexity. The proposed network is composed of three serially connected sub-networks: a cone-to-fan transformation sub-network, a 2D analytical inversion sub-network, and an image refinement sub-network. This provides a comprehensive solution for end-to-end reconstruction for CBCT. The advantages of our method are that the network can simplify a 3D reconstruction problem to a 2D slice-wise reconstruction problem and can complete reconstruction in an end-to-end manner with the system matrix integrated into the network design. Furthermore, reconstruction can be less computationally expensive and easily parallelizable compared with iterative reconstruction methods.     

A numerical technique for analysis of transient two-phase flow in a vertical tube using the Drift Flux Model

This paper presents a numerical solution of one-dimensional transient two-phase flow in a vertical channel using the Drift Flux Model (DFM). The DFM treats the two phases as a mixture, but allows slippage between the gas and the liquid phase. The DFM was used for the calculation of velocity and fraction of each phase, combined with the most relevant closure relationships models for condensation, wall evaporation, and phasic velocities. The solution of the three conservation equations for the mixture and a continuity equation for the gas phases is obtained by a semi-implicit numerical method. A finite volume method is used to discretize the governing equations on a staggered grid in the computational domain. Satisfactory agreement is shown between predicted void fraction, RELAP5 code and available experimental data under both transient and steady state conditions. Numerical solution was also obtained for a wide two-phase flow conditions: system pressure, surface heat flux, mass flow rate and inlet sub-cooling to check the model ability to predict void fraction accurately. It is concluded, therefore, that the DFM is able to predict void fraction in subcooled flow boiling with sufficient accuracy. For pressures lower than 30 bars, the DFM overestimated the void fraction in comparison with the experimental data by about 15%. The model requires less computational power to simulate than other approaches and has no limitations on the nodalization process for numerical stability. It is therefore expected that development of presented model will be useful for the assessment of experimental data, as well as performing pre-test numerical experimentation.     

代数迭代算法进行CT图像重建的研究

对CT代数迭代重建算法(ART)进行了研究,讨论了射线数目对图像重建效果的影响,并采用平滑方法,改善了重建图像质量,加快了收敛速度,得出了效果满意的工业CT图像。