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。     

基于双边滤波迭代修正的CT欠投影ART重建

针对CT欠投影数据进行成像问题,本文提出了一种基于双边滤波迭代修正的代数迭代(ART)重建算法。该算法在每一次迭代过程中,先采用ART算法重建图像并进行非负约束,然后采用双边滤波法对以上约束后的图像进行修正,再进入下一次迭代,直到满足迭代终止条件。为了进一步提高图像重建质量和加快迭代收敛速度,利用改进的双边滤波算法以提高迭代效能。通过对Shepp-Logan体模和真实投影数据进行重建,验证了本文算法的可行性,并与滤波反投影(FBP)算法、ART算法、ART混合高斯滤波(GF-ART)算法相比较。结果表明,本文算法重建出的图像信噪比更高,能够更好的保持图像边缘信息。     

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。     

自适应超分辨率图像的重建算法

背景：超分辨率重建已经在视频、遥感等许多领域内的到广泛的研究与应用。 目的：介绍一种自适应超分辨率重建算法,以期从序列低分辨率图像中重建出高分辨率图像。 方法：采用常数λ=2/3作为正则化参数和自适应步长作为第一种方案。第二种方案充分考虑到低分辨率图像中的运动误差估计、点扩散函数以及加性高斯白噪声对重建算法的影响。实验构造出新的非线性自适应正则化函数,进而利用实验方法分析代价函数的凸性。通过数学理论,根据代价函数凸性实验得到自适应步长因子,从而改进了图像的空间分辨率和算法的收敛速度。 结果与结论：为验证此算法的有效性,采用光学图像进行实验。方案二图像峰值信噪比增高,其收敛速度为方案一的2倍以上;方案二的平均计算需要的时间为68.25 s。结果证实,自适应超分辨率图像重建算法对图像分辨率和迭代的收敛速度均改善显著,其稳定性较好。     

基于L_P范数的磁感应断层成像图像重建算法

磁感应断层成像(MIT)图像重建是一个典型的病态问题,且其数值解不稳定。为了改善解的病态性而又能提高重建图像的质量,本文在变差正则化算法的基础上提出一种新的基于LP范数的变差正则化算法。该算法不仅有效地克服了MIT重建图像数值解的不稳定性,还提高了重建图像的质量,增强了重建图像的空间分辨能力。仿真实验结果表明,该算法所获得的重建图像质量好于Tikhonov正则化算法和变差正则化算法,为MIT提供了一种新的有效方法。     

脑磁源成像中的正则理论

从一个相对完整的正则理论角度对现有的各重建算法进行分析，把它们归属在确定性和随机性正则两大类中。脑内磁源成像中的正则理论，就是通过合理的神经活动特性的相关先验约束，以求得唯一的合理的鲁棒解。中着重讨论了基于Tikhonov正则的最小模和基于Markov随机场模型的hayesian的重建方法。最后，仿真实验进行了两类方法的比较。     

脑磁源成像中的正则理论

从一个相对完整的正则理论角度对现有的各重建算法进行分析，把它们归属在确定性和随机性正则两大类中。脑内磁源成像中的正则理论，就是通过合理的神经活动特性的相关先验约束，以求得唯一的合理的鲁棒解。中着重讨论了基于Tikhonov正则的最小模和基于Markov随机场模型的Bayesian的重建方法。最后，仿真实验进行了两类方法的比较。     

基于非广延熵先验的PET图像重建EI北大核心CSCD

最大化后验(MAP)方法已经被广泛应用于解决图像重建的病态问题。先验项的选择一直是研究的热点,但是传统先验形式往往会导致重建图像模糊或者产生阶梯状伪影。本文针对传统先验形式存在的不足,提出了一种基于非广延熵先验的正电子发射成像(PET)迭代重建方法。该方法主要利用最小化非广延熵先验来消除先验信息和估计图像之间的不确定性。我们将此算法在体模图像上进行了测试,并与基于传统先验的MAP方法比较。实验表明,本文算法能更好抑制噪声,获得较好的重建图像质量。     

基于穿越长度权重反投影重建算法的初步研究

目的：直接反投影是一种快速简便的CT图像重建方法,但由于星形伪影会使图像模糊。为有效地改善CT反投影重建图像的质量,提出一种新的基于穿越长度权重的反投影重建算法,为图像重建提供一种新算法;同时穿越长度的计算方法也能为代数重建算法中的投影系数的计算提供一种新方法。方法：采用VC＋＋6．0工具设计模拟软件,对Shepp-Logan模型进行计算机模拟扫描获得投影数据,同时计算各射线穿越各体素的长度．以穿越长度作为权重对获取的数据进行反投影重建图像。结果：开发出一个具有模拟X-CT扫描与重建功能的软件,该软件能直观地显示传统直接反投影和基于穿越长度权重的反投影重建算法得出的图像,并能对得到的图像进行定量评价和定性分析。结论：基于穿越长度的反投影重建算法能有效地减少星状伪影,提高重建图像的质量,且评价指标（归一化均方距离判据d,归一化平均绝对距离判据r,最坏情况距离判据e）都优于传统的插值法;同时开发出的软件具有可扩展性,为其他算法的实现及比较提供一个良好的平台。     

基于改进型迭代NR的磁感应断层成像图像重建算法

在磁感应断层成像中,图像重建是一个典型的病态问题,其数值解存在不稳定性。针对此问题,提出一种基于加权矩阵和L1范数正则化的改进型迭代Newton-Raphson(NR)算法。该算法通过在目标函数的误差项中引入加权矩阵,同时在L2范数正则化惩罚项的基础上引入L1范数正则化,改善图像重建解的病态性。设置3种典型的模型,分别对有无噪声的数据进行分析,将本算法与Tikhonov正则化算法和迭代NR算法进行对比。在无噪声数据分析中,所提算法相对Tikhonov正则化算法和迭代NR算法的相对图像误差减小0.11~0.14,相关系数提高13%~17%。在有噪声数据中,所提算法相对于Tikhonov正则化算法和迭代NR算法的相对图像误差减小0.06~0.09,相关系数提高7%~10%。提出的算法成像性能较好,且抗噪性能较强,为进一步的实验重建精确性提供理论依据。     

A novel digital tomosynthesis (DTS) reconstruction method using a deformation field map

We developed a novel digital tomosynthesis (DTS) reconstruction method using a deformation field map to optimally estimate volumetric information in DTS images. The deformation field map is solved by using prior information, a deformation model, and new projection data. Patients' previous cone-beam CT (CBCT) or planning CT data are used as the prior information, and the new patient volume to be reconstructed is considered as a deformation of the prior patient volume. The deformation field is solved by minimizing bending energy and maintaining new projection data fidelity using a nonlinear conjugate gradient method. The new patient DTS volume is then obtained by deforming the prior patient CBCT or CT volume according to the solution to the deformation field. This method is novel because it is the first method to combine deformable registration with limited angle image reconstruction. The method was tested in 2D cases using simulated projections of a Shepp-Logan phantom, liver, and head-and-neck patient data. The accuracy of the reconstruction was evaluated by comparing both organ volume and pixel value differences between DTS and CBCT images. In the Shepp-Logan phantom study, the reconstructed pixel signal-to-noise ratio (PSNR) for the 60 degrees DTS image reached 34.3 dB. In the liver patient study, the relative error of the liver volume reconstructed using 60 degrees projections was 3.4%. The reconstructed PSNR for the 60 degrees DTS image reached 23.5 dB. In the head-and-neck patient study, the new method using 60 degrees projections was able to reconstruct the 8.1 degrees rotation of the bony structure with 0.0 degrees error. The reconstructed PSNR for the 60 degrees DTS image reached 24.2 dB. In summary, the new reconstruction method can optimally estimate the volumetric information in DTS images using 60 degrees projections. Preliminary validation of the algorithm showed that it is both technically and clinically feasible for image guidance in radiation therapy.     

基于3D Shepp-Logan头部模型的三维医学图像重建仿真

Shepp-Logan头部模型是计算机断层图像重建(CT)领域仿真计算普遍采用的经典模型。我们提出一种新思路—以3D Shepp-Logan头部模型作为三维医学图像重建领域进行仿真实验和算法性能评测的基本参考模型。首先介绍了3D Shepp-Logan头部模型的设计与实现以及仿真投影数据的计算,进而描述了所设计的三维医学图像重建仿真计算过程。数值实验部分给出了基于3D Shepp-Logan头部模型的三维医学图像重建仿真实验。实验结果表明了新思路的可行性和模型计算的准确性。     

An approximate reconstruction method for helical cone-beam differential phase-contrast computed tomography images

Differential phase-contrast computed tomography (DPC-CT) is a novel x-ray inspection method. Currently, DPC-CT reconstruction problems are solved by using parallel-beam, fan-beam and cone-beam algorithms. The above algorithms cannot show the internal structures of rod-shaped objects well enough for only reconstructing a few slices. The helical cone-beam algorithms have significant advantages for rod-shaped objects over other algorithms. Along with our numerical evaluation and verification, we report a PI-line-based approximate algorithm for helical cone-beam DPC-CT, which can be applied to reconstruct the refractive index decrement distribution of the samples directly from phase-contrast projection images. Simulations using a 3D Shepp-Logan phantom are carried out to verify the proposed algorithm. Reconstruction results show that the proposed algorithm can provide higher quality performance compared with the existing interpolation-based reconstruction algorithm.     

Analyser-based mammography using single-image reconstruction

We implement an algorithm that is able to decode a single analyser-based x-ray phase-contrast image of a sample, converting it into an equivalent conventional absorption-contrast radiograph. The algorithm assumes the projection approximation for x-ray propagation in a single-material object embedded in a substrate of approximately uniform thickness. Unlike the phase-contrast images, which have both directional bias and a bias towards edges present in the sample, the reconstructed images are directly interpretable in terms of the projected absorption coefficient of the sample. The technique was applied to a Leeds TOR[MAM] phantom, which is designed to test mammogram quality by the inclusion of simulated microcalcifications, filaments and circular discs. This phantom was imaged at varying doses using three modalities: analyser-based synchrotron phase-contrast images converted to equivalent absorption radiographs using our algorithm, slot-scanned synchrotron imaging and imaging using a conventional mammography unit. Features in the resulting images were then assigned a quality score by volunteers. The single-image reconstruction method achieved higher scores at equivalent and lower doses than the conventional mammography images, but no improvement of visualization of the simulated microcalcifications, and some degradation in image quality at reduced doses for filament features.     

Scatter kernel estimation with an edge-spread function method for cone-beam computed tomography imaging

The clinical applications of kilovoltage x-ray cone-beam computed tomography (CBCT) have been compromised by the limited quality of CBCT images, which typically is due to a substantial scatter component in the projection data. In this paper, we describe an experimental method of deriving the scatter kernel of a CBCT imaging system. The estimated scatter kernel can be used to remove the scatter component from the CBCT projection images, thus improving the quality of the reconstructed image. The scattered radiation was approximated as depth-dependent, pencil-beam kernels, which were derived using an edge-spread function (ESF) method. The ESF geometry was achieved with a half-beam block created by a 3 mm thick lead sheet placed on a stack of slab solid-water phantoms. Measurements for ten water-equivalent thicknesses (WET) ranging from 0 cm to 41 cm were taken with (half-blocked) and without (unblocked) the lead sheet, and corresponding pencil-beam scatter kernels or point-spread functions (PSFs) were then derived without assuming any empirical trial function. The derived scatter kernels were verified with phantom studies. Scatter correction was then incorporated into the reconstruction process to improve image quality. For a 32 cm diameter cylinder phantom, the flatness of the reconstructed image was improved from 22% to 5%. When the method was applied to CBCT images for patients undergoing image-guided therapy of the pelvis and lung, the variation in selected regions of interest (ROIs) was reduced from >300 HU to <100 HU. We conclude that the scatter reduction technique utilizing the scatter kernel effectively suppresses the artifact caused by scatter in CBCT.     

Feasibility of volume-of-interest (VOI) scanning technique in cone beam breast CT--a preliminary study

This work is to demonstrate that high quality cone beam CT images can be generated for a volume of interest (VOI) and to investigate the exposure reduction effect, dose saving, and scatter reduction with the VOI scanning technique. The VOI scanning technique involves inserting a filtering mask between the x-ray source and the breast during image acquisition. The mask has an opening to allow full x-ray exposure to be delivered to a preselected VOI and a lower, filtered exposure to the region outside the VOI. To investigate the effects of increased noise due to reduced exposure outside the VOI on the reconstructed VOI image, we directly extracted the projection data inside the VOI from the full-field projection data and added additional data to the projection outside the VOI to simulate the relative noise increase due to reduced exposure. The nonuniform reference images were simulated in an identical manner to normalize the projection images and measure the x-ray attenuation factor for the object. Regular Feldkamp-Davis-Kress filtered backprojection algorithm was used to reconstruct the 3D images. The noise level inside the VOI was evaluated and compared with that of the full-field higher exposure image. Calcifications phantom and low contrast phantom were imaged. Dose reduction was investigated by estimating the dose distribution in a cylindrical water phantom using Monte Carlo simulation based Geant4 package. Scatter reduction at the detector input was also studied. Our results show that with the exposure level reduced by the VOI mask, the dose levels were significantly reduced both inside and outside the VOI without compromising the accuracy of image reconstruction, allowing for the VOI to be imaged with more clarity and helping to reduce the breast dose. The contrast-to-noise ratio inside the VOI was improved. The VOI images were not adversely affected by noisier projection data outside the VOI. Scatter intensities at the detector input were also shown to decrease significantly both inside and outside the VOI in the projection images, indicating potential improvement of image quality inside the VOI and contribution to dose reduction both inside and outside the VOI.     

Respiratory correlated cone-beam computed tomography on an isocentric C-arm

A methodology for 3D image reconstruction from retrospectively gated cone-beam CT projection data has been developed. A mobile x-ray cone-beam device consisting of an isocentric C-arm equipped with a flat panel detector was used to image a moving phantom. Frames for reconstruction were retrospectively selected from complete datasets based on the known rotation of the C-arm and a signal from a respiratory monitor. Different sizes of gating windows were tested. A numerical criterion for blur on the reconstructed image was suggested. The criterion is based on minimization of an Ising energy function, similar to approaches used in image segmentation or restoration. It is shown that this criterion can be used for the determination of the optimal gating window size. Images reconstructed from the retrospectively gated projection sequences using the optimal gating window data showed a significant improvement compared to images reconstructed from the complete projection datasets.     

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。     

基于混合正则化算法的颅内异物电阻抗成像仿真研究

为提高电阻抗静态重构图像的质量,研究将离散变差函数引入到重构算法中,形成混合正则化重构算法,并对计及颅骨的颅内异物进行了重构成像。与常用的Tikhonov正则化算法相比,混合正则化重构算法对重构信息的分辨能力显著提高,能有效克服低电导率颅骨对颅内信息的屏蔽效应,显著改善所得重构图像质量,与设定病例的医学图像相符。这一成果提高了电阻抗静态成像技术在颅内异物定位方面的质量,为电阻抗静态成像技术的实用化打下了基础。