低剂量CT投影图像噪声分析及去噪算法研究

提高低剂量CT图像的信噪比(SNR)是使低剂量CT获得有效临床应用的关键。本文对低剂量CT投影数据噪声研究发现,在投影图像的某些区域中可能会存在一些孤立的噪声点,滤除这些孤立点后的投影数据近似服从非平稳高斯噪声分布。由此,提出一种低剂量CT图像降噪算法,包括"孤立点"检测与滤波(IDE),基于最大后验概率(MAP)的高斯噪声滤波及FBP重建过程。计算机仿真以及真实数据实验表明,本文提出的去噪算法获得的重建CT图像,SNR及视觉效果均有明显的提高。     

基于全变分α散度最小化的PET优质重建

为了获得优质的PET成像,本文提出一种基于全变分阿尔法散度最小化的PET重建新方法.新方法通过引入阿尔法散度度量投影数据和估计值之间的偏差;通过增加全变分正则化修正阿尔法散度最小化解的一致性.针对新构建的PET重建目标函数的求解,本文提出一种基于次梯度理论的交替式迭代策略,期间运用自适应非单调线性搜索来保证算法的收敛性.仿真和临床PET数据实验表明,本文方法在噪声抑制和边缘保持方面均优于传统的PET重建方法.     

基于伪Zernike旋转矩的低剂量CT图像重建方法

本文提出了一种基于伪Zernike旋转矩的低剂量CT(Com puted Tomography)图像重建新方法,该方法首先构建了扇形束投影数据和伪Zernike旋转矩之间的关系,然后利用这种关系从已知投影数据中估计出未知投影数据,从而达到在低剂量放射线条件下提高重建图像质量的目的。实验证明,新方法可以有效地估计出未知投影数据,并能获得更好的重建结果。     

低剂量CT重建中的双边滤波权值优化新方法

为了提升低剂量CT重建图像质量,本文提出了一种基于投影数据恢复导引的双边滤波权值优化方法.新方法有效地将CT投影数据恢复和图像数据恢复的两种低剂量成像策略进行结合,实现优质的低剂量CT重建.具体而言,本文中投影数据恢复采用三维块匹配滤波进行,图像数据恢复采用双边滤波进行,其中双边滤波权值进行优化设计.在双边滤波权值设计...     

基于全广义变分约束加权最小二乘的低剂量计算机断层重建方法

为了减少X射线的辐射剂量，提出了一种基于全广义变分约束加权最小二乘的低剂量计算机断层（CT）重建方法。首先对投影数据进行统计建模，然后将全广义变分正则化作为先验信息引入到投影数据恢复过程中，从而达到抑制噪声的目的，最后使用传统的滤波反投影算法进行CT图像重建。在Shepp-Logan体模实验中，提出方法的重建结果与Gibbs先验约束的惩罚加权最小二乘（Gibbs-WLS）、字典学习先验约束的惩罚加权最小二乘（DL-WLS）和全变分先验约束的惩罚加权最小二乘（TV-WLS）方法的重建结果相比，均方根误差分别降低了25.06%、1.50%和15.21%，信噪比分别提高了10.29%、0.53%和5.68%。在Clock体模实验中，提出方法的重建结果与Gibbs-WLS、DL-WLS和TV-WLS方法的重建结果相比，均方根误差分别降低了42.72%、23.45%和34.63%，信噪比分别提高了27.04%、11.42%和15.49%。实验结果表明，该方法在有效抑制低剂量CT图像的伪影和噪声的同时可以很好地保持图像的边缘信息和结构细节特征。     

基于梯度保真项的低剂量CT统计迭代重建算法

针对低剂量计算机断层扫描(Computed Tomography,CT)重建图像时容易出现明显条形伪影这一现象,提出一种基于梯度保真项的低剂量CT统计迭代重建算法。该算法克服了原始全变分(Total Variation,TV)模型在抑制条形伪影和噪声的同时引入阶梯效应的缺点,首先把梯度保真约束项和能够区分图像平滑区和细节区的边缘指示函数应用到TV模型中得到基于梯度保真项的自适应全变分模型,然后再把新模型与惩罚加权最小二乘(Penalized Weighted Least Square,PWLS)重建算法相结合,使用交替方向迭代法得到最终的图像。采用Shepp-Logan模型来验证算法的有效性,实验结果表明,该算法不仅可以有效地去除条形伪影,还可以较好地保护图像的边缘和细节信息。     

缺失投影数据的估计研究

在CT图像重建中,由于CT设备本身的结构和重建算法的局限性以及病人自主或者非自主的运动破坏了投影数据的一致性和完整性。当投影数据采集或投影角度不完全时,通常采用代数重建算法(ART)及其改进算法进行重建。但由于ART算法运行速度较慢,耗时较多。本文从恢复缺失的投影角度出发,通过比较不同的插值方法,采用双线性插值法对不完全角度下的或缺失的投影数据进行估计,得到了一定的成效,并对其投影图像进行恢复,从而缩短了运行时间。     

基于点探测器和柱面源双位置扫描的直接体积CT的研究

目前直接体积CT主要存在两大困难:一是如何获得三维图像精确重建所需的投影数据,包括扫描方式的可实现性;二是如何尽量避免康普顿散射对重建图像质量的影响.针对这些问题,本文提出一种新型的直接体积CT成像模式,即采用X线栅形扫描的柱面源、一组分布在大圆和垂直圆弧上的多个点状探测器采集数据,通过柱面源的一次旋转即可得到完全的投影数据.本文对该扫描装置的结构中X线柱面源的形状和尺寸、探测器的个数和位置分布进行了详细的说明,并对该装置的完全性条件进行论证.然后结合此扫描结构的特点,给出一种三维图像重建算法.计算机仿真实验的结果表明,该扫描结构在保证投影数据完全的条件下,实现了机械转动次数最少、有效抑制康普顿散射、提高三维图像重建速度和精度的目的,使直接体积CT的成像速度和重建精度比现有模式大大提高.     

稀疏角度CT图像重建的Huber-TV正则化方法

对于稀疏角度下的投影数据，计算机断层扫描重建图像容易出现分辨率低、伪影较多的问题，难以满足工业及医学诊断要求。文中从迭代重建的角度出发，提出一个结合全变分（TV）和Huber函数（Huber-TV）的CT重建方法。该方法利用Huber函数替代传统全变分模型中的L1范数，在合理控制函数阈值的条件下，充分利用Huber函数的线性部分对大于阈值的梯度图像进行较轻的惩罚，以保持图像边缘连续性；再结合二次项对小于阈值的梯度图像进行较大的惩罚，以抑制图像中不连续梯度跳跃。新模型目标函数的光滑性可以使得梯度下降法快速收敛到最优值，避开传统全变分模型中的次梯度计算，从而降低计算复杂度并加快迭代速度。实验结果表明，在稀疏角度重建条件下，与传统TV模型相比，Huber-TV模型的均方根误差降低19%，信噪比提升22.33 dB，说明所提方法高效可行。     

基于EM算法的低剂量CT图像去噪

提高低剂量CT图像的信噪比是使其获得有效临床应用的关键.文中针对低剂量CT投影数据极低信噪比特性以及投影数据噪声所特有的非平稳高斯特性,提出采用EM(Expectation-Maximization)算法通过求解图像后验概率的条件期望值最大的方法达到图像复原目的,同时在算法中实现了图像模型参数的估计,并且引入Gibbs采样技术,很好的解决了算法计算问题.计算机仿真及真实投影数据的实验表明,本文算法无论从复原图像的可视化效果上还是从噪声-分辨率关系的定量分析上,都具有一定优势.     

低剂量X射线CT重建算法仿真分析

对Shepp-Logan头部图像模型提供的原始图像进行低剂量X射线计算机断层成像（CT,Computed Tomography）平移/旋转扫描,利用所得数据对图像的统计重建算法进行仿真。将仿真结果与传统的滤波反投影重建算法的重建结果进行比较,并分别将两种算法的重建图像与原图像进行比较。通过比较得出,滤波反投影重建算法不能有效重建低剂量CT图像,而统计重建算法重建效果优于前者,能够较好地恢复原图像,从而能够适用于低剂量条件下的CT图像重建。     

Low-Dose X-ray CT Reconstruction via Dictionary Learning

Although diagnostic medical imaging provides enormous benefits in the early detection and accuracy diagnosis of various diseases, there are growing concerns on the potential side effect of radiation induced genetic, cancerous and other diseases. How to reduce radiation dose while maintaining the diagnostic performance is a major challenge in the computed tomography (CT) field. Inspired by the compressive sensing theory, the sparse constraint in terms of total variation (TV) minimization has already led to promising results for low-dose CT reconstruction. Compared to the discrete gradient transform used in the TV method, dictionary learning is proven to be an effective way for sparse representation. On the other hand, it is important to consider the statistical property of projection data in the low-dose CT case. Recently, we have developed a dictionary learning based approach for low-dose X-ray CT. In this paper, we present this method in detail and evaluate it in experiments. In our method, the sparse constraint in terms of a redundant dictionary is incorporated into an objective function in a statistical iterative reconstruction framework. The dictionary can be either predetermined before an image reconstruction task or adaptively defined during the reconstruction process. An alternating minimization scheme is developed to minimize the objective function. Our approach is evaluated with low-dose X-ray projections collected in animal and human CT studies, and the improvement associated with dictionary learning is quantified relative to filtered backprojection and TV-based reconstructions. The results show that the proposed approach might produce better images with lower noise and more detailed structural features in our selected cases. However, there is no proof that this is true for all kinds of structures.     

X-ray CT metal artifact reduction using wavelets: an application for imaging total hip prostheses

Traditional computed tomography (CT) reconstructions of total joint prostheses are limited by metal artifacts from corrupted projection data. Published metal artifact reduction methods are based on the assumption that severe attenuation of X-rays by prostheses renders corresponding portions of projection data unavailable, hence the "missing" data are either avoided (in iterative reconstruction) or interpolated (in filtered backprojection with data completion; typically, with filling data "gaps" via linear functions). In this paper, we propose a wavelet-based multiresolution analysis method for metal artifact reduction, in which information is extracted from corrupted projection data. The wavelet method improves image quality by a successive interpolation in the wavelet domain. Theoretical analysis and experimental results demonstrate that the metal artifacts due to both photon starving and beam hardening can be effectively suppressed using our method. As compared to the filtered backprojection after linear interpolation, the wavelet-based reconstruction is significantly more accurate for depiction of anatomical structures, especially in the immediate neighborhood of the prostheses. This superior imaging precision is highly advantageous in geometric modeling for fitting hip prostheses.     

Enhanced localized computerized tomography employing the discrete wavelet transform

A new localized computerized tomography technique based on the multiresolution analysis (MRA) implementation of the discrete wavelet transform is proposed. Our technique is based upon viewing the projection data as a set of one-dimensional functions of the space variablet and decomposing each one into an approximation signal and a set of detail signals using MRA. The approximation signal and detiil signals associated with each projection are filtered using the ramp filter || of the standard reconstruction technique filtered back projection to generate the set of filtered projections. It is shown that only a very sparse set of projection data outside of the region of interest (ROI) is required to reconstruct a high-quality image of the ROI and a reasonable image outside of the ROI. Simulation results using the Shepp-Logan head phantom are presented to demonstrate the proposed technique.     

Handling of long objects in iterative improvement of nonexact reconstruction in helical cone-beam CT

In medical helical cone-beam CT, it is common that the region-of-interest (ROI) is contained inside the helix cylinder, while the complete object is long and extends outside the top and the bottom of the cylinder. This is the Long Object Problem. Analytical reconstruction methods for helical cone-beam CT have been designed to handle this problem. It has been shown that a moderate amount of over-scanning is sufficient for reconstruction of a certain ROI. The over-scanning projection rays travel both through the ROI, as well as outside the ROI. This is unfortunate for iterative methods since it seems impossible to compute accurate values for the projection rays which travel partly inside and partly outside the ROI. Therefore, it seems that the useful ROI will diminish for every iteration step. We propose the following solution to the problem. First, we reconstruct volume regions also outside the ROI. These volume regions will certainly be incompletely reconstructed, but our experimental results show that they serve well for projection generation. This is rather counter-intuitive and contradictory to our initial assumptions. Second, we use careful extrapolation and masking of projection data. This is not a general necessity, but needed for the chosen iterative algorithm, which includes rebinning and iterative filtered backprojection. Our idea here was to use an approximate reconstruction method which gives cone-beam artifacts and then improve the reconstructed result by iterative filtered backprojection. The experimental results seem very encouraging. The cone-beam artifacts can indeed be removed. Even voxels close to the boundary of the ROI are as well enhanced by the iterative loop as those in the middle of the ROI.     

Wavelets, ridgelets, and curvelets for Poisson noise removal.

In order to denoise Poisson count data, we introduce a variance stabilizing transform (VST) applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant variance. This new transform, which can be deemed as an extension of the Anscombe transform to filtered data, is simple, fast, and efficient in (very) low-count situations. We combine this VST with the filter banks of wavelets, ridgelets and curvelets, leading to multiscale VSTs (MS-VSTs) and nonlinear decomposition schemes. By doing so, the noise-contaminated coefficients of these MS-VST-modified transforms are asymptotically normally distributed with known variances. A classical hypothesis-testing framework is adopted to detect the significant coefficients, and a sparsity-driven iterative scheme reconstructs properly the final estimate. A range of examples show the power of this MS-VST approach for recovering important structures of various morphologies in (very) low-count images. These results also demonstrate that the MS-VST approach is competitive relative to many existing denoising methods.     

Iterative deblurring for CT metal artifact reduction

Iterative deblurring methods using the expectation maximization (EM) formulation and the algebraic reconstruction technique (ART), respectively, are adapted for metal artifact reduction in medical computed tomography (CT). In experiments with synthetic noise-free and additive noisy projection data of dental phantoms, it is found that both simultaneous iterative algorithms produce superior image quality as compared to filtered backprojection after linearly fitting projection gaps. Furthermore, the EM-type algorithm converges faster than the ART-type algorithm in terms of either the I-divergence or Euclidean distance between ideal and reprojected data in the authors' simulation. Also, for a given iteration number, the EM-type deblurring method produces better image clarity but stronger noise than the ART-type reconstruction. The computational complexity of EM- and ART-based iterative deblurring is essentially the same, dominated by reprojection and backprojection. Relevant practical and theoretical issues are discussed.     

A cone-beam reconstruction algorithm for circle-plus-arc data-acquisition geometry

In cone-beam computerized tomography (CT), projections acquired with the focal spot constrained on a planar orbit cannot provide a complete set of data to reconstruct the object function exactly. There are severe distortions in the reconstructed noncentral transverse planes when the cone angle is large. In this work, a new method is proposed which can obtain a complete set of data by acquiring cone-beam projections along a circle-plus-arc orbit. A reconstruction algorithm using this circle-plus-arc orbit is developed, based on the Radon transform and Grangeat's formula. This algorithm first transforms the cone-beam projection data of an object to the first derivative of the three-dimensional (3-D) Radon transform, using Grangeat's formula, and then reconstructs the object using the inverse Radon transform. In order to reduce interpolation errors, new rebinning equations have been derived accurately, which allows one-dimensional (1-D) interpolation to be used in the rebinning process instead of 3-D interpolation. A noise-free Defrise phantom and a Poisson noise-added Shepp-Logan phantom were simulated and reconstructed for algorithm validation. The results from the computer simulation indicate that the new cone-beam data-acquisition scheme can provide a complete set of projection data and the image reconstruction algorithm can achieve exact reconstruction. Potentially, the algorithm can be applied in practice for both a standard CT gantry-based volume tomographic imaging system and a C-arm-based cone-beam tomographic imaging system, with little mechanical modification required.