轴对称物体X射线层析成像的变分模型与算法

On some variational models and their algorithms for axially symmetric objects tomography from a single X-ray source

本文介绍了用X射线投影进行轴对称物体密度重建的一些新二维变分模型与其数值计算方法,从而推广了先前球对称物体密度重建的一维工作.由于直接解这一类数学模型转化的非线性代数方程组,数值实现难度大,本文给出了易实现的增广Lagrange解法,这种方法不仅有利于处理高阶正则化,而且在X光图像有额外模糊的情形下,自动提供了有用的中间量正则化;也给出了一些初步的仿真计算结果.本工作为下一步研究三维非对称物体密度重建打下基础.

In this paper, we present some variational models and their computational algorithms to reconstruct density distribution of an axially symmetric object by X-ray radiographs, generalising previous works on spheri- cally symmetric objects. Since effective numerical solution of the nonlinear systems generated from these models remains a mathematical challenge, the proposed use of an augmented Lagrangian method enables incorporation of high order regularizers and an automatic adding of regularization in the case of additional blurring. Some preliminary tests are conducted. This work lays the foundation for future works to model 3D non-symmetric objects by X-ray radiographs.