基于非线性相位恢复的X射线相位衬度断层成像算法  

An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval

作　　者：倪文磊[1] 周铁[1] 

机构地区：[1]北京大学数学科学学院,北京100871

出　　处：《应用数学和力学》2008年第1期93-103,共11页Applied Mathematics and Mechanics

基　　金：科技部国家重点基础研究发展计划资助项目(2003CB716101);国家自然科学基金(重点)资助项目(60532080);教育部科学研究重大资助项目(306017)

摘　　要：对全息测量下的X射线相位衬度断层成像问题提出了一种新的重建算法.该算法的主要想法是利用牛顿迭代法求解非线性的相位恢复问题.我们证明了牛顿方向满足的线性方程是非适定的,并利用共轭梯度法得到方程的正则化解.最后利用模拟数据进行了数值实验,数值结果验证了算法的合理性以及对噪声数据的数值稳定性,同时通过与线性化相位恢复算法的数值结果比较说明了新算法对探测数据不要求限制在Fresnel区域的近场,适用范围更广.A new algorithm for phase contrast X-ray tomography under holographic measurement was proposed. The main idea of the algorithm was to solve the nonlinear phase retrieval problem using the Newton iterative method. The linear equations for the Newton directions were proved to be hi-posed and the regularized solutions were obtained by the conjugate gradient method. Some numerical experimeres with computer simulated data were presented.The efficiency, feasibility and the numerical stability of the algorithm were illustrated by the numerical experiments. Compared with the resuIts produced by the linearized phase retrieval algorithm, it can be seen that the new algorithm is not limited to be only efficient for the data measured in the near-field of the Fresnel region and thus it has a broader validity range.

关 键 词：相位衬度断层成像 全息测量 相位恢复 

分 类 号：O29[理学—应用数学] O434.19[理学—数学]