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Development of fast image reconstruction technique for CT image using active nonlinear dynamics of iterative method

基于迭代法的主动非线性动力学CT图像快速图像重建技术的发展

基本信息

批准号：
18560412
负责人：
YOSHINAGA Tetsuya
金额：
$ 1.16万
依托单位：
The University of Tokushima
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18560412/
关键词：
CT Image Reconstruction Nonlinear Dynamical System Bifurcation Iterative Method Medical Imaging Equipments

项目摘要

Iterative reconstruction is a well known method of reconstructing computed tomography (CT) images, and it has advantages over the filtered back-projection procedure, which is commonly used for CT reconstruction in medical practices, in reducing artifacts. Because of the high quality of these reconstructions, a lot of research has been done on improving the iterative deblurring procedures. Of the iterative reconstruction algorithms, the power multiplicative algebraic reconstruction technique (PMART) has good properties for maximizing entropy ; however, it requires a large number of iterations to obtain the final reconstructed image for large data sets.The final reconstructed image obtained by applying an iterative reconstruction algorithm for appropriate initial pixel values corresponds to a fixed or periodic point observed in the dynamical system describing the iterative reconstruction technique. Our bifurcation analysis of PMART with multiple pixels enabled us to observe various kinds … More of nonlinear phenomena such as the coexistence of a false image, the transition of stability of fixed points, and the generation of a two-periodic point, by changing one of the system parameters. The results also suggest appropriate parameter regions and phantom-image values within the PMART can operate normally.To improve the speed of convergence, we propose an extended PMART, which is a dynamical class that includes the multiplicative algebraic reconstruction technique (MART) as well as PMART. The process of convergence for iterative points in the neighborhood of a reconstructed image can be reduced to the property of the characteristic multiplier of a stable fixed point observed in the dynamical system. To investigate the behavior of convergence, we present a computational method of obtaining parameter sets in which the given real or absolute values of the characteristic multiplier are equal. The advantage of the extended PMART is verified by comparing it with the standard MART using numerical experiments. Less

迭代重建是一种众所周知的重建计算机断层扫描 (CT) 图像的方法，与医疗实践中常用于 CT 重建的滤波反投影程序相比，它在减少伪影方面具有优势。由于这些重建的高质量，人们在改进迭代去模糊过程方面进行了大量的研究。在迭代重建算法中，幂乘代数重建技术（PMART）具有良好的熵最大化特性；然而，对于大数据集，它需要大量的迭代才能获得最终的重建图像。通过对适当的初始像素值应用迭代重建算法获得的最终重建图像对应于描述迭代重建技术的动态系统中观察到的固定或周期点。我们对多像素 PMART 的分岔分析使我们能够通过改变系统参数之一来观察各种非线性现象，例如假图像的共存、不动点稳定性的转变以及二周期点的生成。结果还表明，PMART 内适当的参数区域和幻影图像值可以正常运行。为了提高收敛速度，我们提出了一种扩展的 PMART，它是一个动态类，包括乘法代数重建技术 (MART) 以及 PMART。重建图像邻域内迭代点的收敛过程可以简化为动态系统中观察到的稳定不动点的特征乘数的性质。为了研究收敛行为，我们提出了一种获取参数集的计算方法，其中特征乘数的给定实数或绝对值相等。通过数值实验将扩展PMART与标准MART进行比较，验证了扩展PMART的优势。较少的