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A Fast Iterative Method with Algebraic CT Image Reconstruction Technique Based on Dynamical System Theory

基于动力系统理论的代数CT图像重建技术的快速迭代方法

基本信息

批准号：
14550420
负责人：
YOSHINAGA Tetsuya
金额：
$ 0.77万
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：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

项目摘要

The simultaneous iterative reconstruction technique (SIRT) is known as a method to reconstruct images of X-ray computerized tomography (CT). Iterative deblurring methods using the algebraic reconstruction technique (ART) and the expectation maximization (EM) formulation have advantages for reducing artifacts against the filtered backprojection procedure, which is commonly used for CT reconstruction in practice. Because of the high-quality reconstructions, there has been a lot of research improving the SIRT procedures. However, each type of SIRT requires a large number of iterations to obtain the final reconstruction image.On the other hand, the iterative formulae of SIRT can be considered as a dynamical system of reconstruction grid elements in the N-dimensional state space, where N is the number of pixels. Then a stable fixed point of the system corresponds to the image to be reconstructed. Moreover the dynamics in the neighborhood of the fixed point govern the convergence speed of the SIRT procedure. In this study, we investigate properties of the system from the viewpoint of dynamical system theory, and examine a numerical method for solving a fixed point of the system, using a shooting method such as Newton's method. In the study period, we found that the proposed method gives rise to the very fast convergence for the reconstruction. The efficiency was illustrated using experiments with synthetic additive noise projection data from a phantom including a metal part.

同步迭代重建技术（SIRT）是一种重建x射线计算机断层扫描（CT）图像的方法。使用代数重建技术（ART）和期望最大化（EM）公式的迭代去模糊方法在减少对实际中常用的过滤反投影过程的伪影方面具有优势。由于高质量的重建，有很多研究改进了SIRT程序。然而，每种类型的SIRT都需要大量的迭代才能获得最终的重建图像。另一方面，SIRT的迭代公式可以看作是N维状态空间中重构网格元素的动态系统，其中N为像素数。然后系统的一个稳定不动点对应于待重构图像。此外，不动点附近的动态控制了SIRT过程的收敛速度。本文从动力系统理论的角度研究了系统的性质，并研究了一种求解系统不动点的数值方法，即牛顿法等射击法。在研究过程中，我们发现该方法具有较快的重构收敛性。用含金属零件的模拟体的合成加性噪声投影数据实验说明了该方法的有效性。