Fast parallel algorithm for three-dimensional distance-driven model in iterative computed tomography reconstruction

The projection matrix model is used to describe the physical relationship between reconstructed object and projection.Such a model has a strong influence on projection and backprojection,two vital operations in iterative computed tomographic reconstruction.The distance-driven model(DDM) is a state-of-the-art technology that simulates forward and back projections.This model has a low computational complexity and a relatively high spatial resolution;however,it includes only a few methods in a parallel operation with a matched model scheme.This study introduces a fast and parallelizable algorithm to improve the traditional DDM for computing the parallel projection and backprojection operations.Our proposed model has been implemented on a GPU(graphic processing unit) platform and has achieved satisfactory computational efficiency with no approximation.The runtime for the projection and backprojection operations with our model is approximately 4.5 s and 10.5 s per loop,respectively,with an image size of 256×256×256 and 360 projections with a size of 512×512.We compare several general algorithms that have been proposed for maximizing GPU efficiency by using the unmatched projection/backprojection models in a parallel computation.The imaging resolution is not sacrificed and remains accurate during computed tomographic reconstruction.     

双即插即用能谱计算机断层重建算法

为降低X射线辐射剂量和提高成像效率,开发准确和高效的多能谱成像方法,提出一种具有双即插即用（PnP）框架的图像重建方法。该方法引入两个PnP正则化能量函数,分别对多通道图像内蕴低秩性与通道内图像稀疏性进行度量。首先以多通道图像间的相似块构造高维张量,然后引入张量加权核范数对张量低秩性进行刻画,并结合图像梯度域L0（伪）范数对通道内图像稀疏性进行刻画,最后设计基于交替方向乘子法的高效求解算法。为验证算法的可行性,开展模拟多通道光子计数采样图像重建实验。实验结果表明：与现有代表性方法相比,所提方法的峰值信噪比提升0.067 dB～1.89 dB,时间消耗约为代表性方法的25%;所提方法具有抑制伪影干扰和改善图像质量的优势,并且计算效率得到显著提升。     

An algorithm for computed tomography image reconstruction from limited-view projections

<正>With the development of the compressive sensing theory,the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology.This paper develops an iterative algorithm for image reconstruction,which can fit most cases.This method gives an image reconstruction flow with the difference image vector,which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough.Then the l_2-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles.The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data.Moreover,all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.     

非精确交替方向总变分最小化重建算法

CT (computed tomography)系统实际应用当中, 经常会出现扫描数据不满足数据完备性条件的情况. 针对不完全角度重建问题的研究, 是目前迭代型算法研究中的一个热点. 一系列基于带有约束的总变分最小化的重建算法近年来在不完全角度重建中取得了较好的效果, 这其中基于交替方向法 (alternating direction method, ADM) 的重建算法表现出更好的性能. 然而, ADM方法在求解过程中对矩阵求逆的处理效率不高, 导致极大的计算开销. 本文针对该问题, 使用非精确ADM方法, 利用线性近似的方式替换掉计算开销较大的项, 使得矩阵求逆问题可以通过快速傅里叶变换加速实现. 实验结果表明, 本文提出的非精确交替方向总变分最小化重建算法与精确ADM重建算法相比, 没有明显的精度损失, 计算时间缩减30%左右. 关键词： 不完全角度重建 总变分最小化 非精确交替方向法     

A Compton scattering image reconstruction algorithm based on total variation minimization

Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process.The reconstruction problem of Compton scattering imaging is the inverse problem to solve electron densities from nonlinear equations,which is ill-posed.This means the solution exhibits instability and sensitivity to noise or erroneous measurements.Using the theory for reconstruction of sparse images,a reconstruction algorithm based on total variation minimization is proposed.The reconstruction problem is described as an optimization problem with nonlinear data-consistency constraint.The simulated results show that the proposed algorithm could reduce reconstruction error and improve image quality,especially when there are not enough measurements.     

基于动态时间弯曲的X射线变电流投影融合方法

针对变电流投影融合中的阈值选择问题,提出了一种基于动态时间弯曲的变电流投影融合方法.该方法首先计算不同电流下投影的灰度值-有效边缘梯度序列,然后利用动态时间弯曲距离对预处理后的序列进行相似匹配,自动判断最佳融合阈值,最后根据阈值确定不同电流投影的子区域并对其进行融合,实现了探测器动态范围的扩展.本文方法计算的各角度下融合阈值的平均误差仅为2.26%,能够避免人工选择融合阈值的主观性,基于融合后重建图像的信噪比与几何尺寸测量准确度均优于固定融合阈值的方法.     

Fast local reconstruction by selective backprojection for low dose in dental computed tomography

The high radiation dose in computed tomography （CT） scans increases the lifetime risk of cancer, which becomes a major clinical concern. The backprojection-filtration （BPF） algorithm could reduce the radiation dose by reconstructing the images from truncated data in a short scan. In a dental CT, it could reduce the radiation dose for the teeth by using the projection acquired in a short scan, and could avoid irradiation to the other part by using truncated projection. However, the limit of integration for backprojection varies per PI-line, resulting in low calculation efficiency and poor parallel performance. Recently, a tent BPF has been proposed to improve the calculation efficiency by rearranging the projection. However, the memory-consuming data rebinning process is included. Accordingly, the selective BPF （S-BPF） algorithm is proposed in this paper. In this algorithm, the derivative of the projection is backprojected to the points whose x coordinate is less than that of the source focal spot to obtain the differentiated backprojection. The finite Hilbert inverse is then applied to each PI-line segment. S-BPF avoids the influence of the variable limit of integration by selective backprojection without additional time cost or memory cost. The simulation experiment and the real experiment demonstrated the higher reconstruction efficiency of S-BPF.     

基于卷积法TV模型的锥束CT散射校正方法

为了解决CT图像中散射伪影问题,提出并使用修正的泊松分布函数作为散射函数,然后利用卷积模型生成多个散射基图像,将基图像与原始重建图像的线性组合作为最终重建图像,最后,通过使重建图像的全变分函数最小求取线性组合系数最优解。该算法具有计算复杂度小、能够灵活应用于不同的成像对象的特点。实验结果表明,算法能够有效抑制散射导致的杯状和黑色带状伪影,提高图像对比度。     

锥束CT系统旋转平移轨迹几何参数标定方法

针对锥束CT系统旋转平移（RT）轨迹中几何参数难以直接测量的问题,在单圆轨迹标定方法的基础上,提出了一种适用于RT轨迹的几何参数标定方法。该方法利用定标体模投影轨迹的椭圆参数与系统几何参数建立关系,解析求解出系统的内部参数。在此基础上,外推得到旋转轴所有的位置参数,并求得符合理想轨迹要求的几何参数。所求参数都可以通过解析的公式得到,能有效避免迭代法陷入局部最优的问题。对存在偏差的系统进行了仿真,并利用该方法进行标定,实验结果表明,该方法能有效抑制由于几何参数误差造成的几何伪影,提高图像质量。