## 留言板

 引用本文: 倪文磊, 周铁. 基于非线性相位恢复的X射线相位衬度断层成像算法[J]. 应用数学和力学, 2008, 29(1): 93-103.
NI Wen-lei, ZHOU Tie. An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval[J]. Applied Mathematics and Mechanics, 2008, 29(1): 93-103.
 Citation: NI Wen-lei, ZHOU Tie. An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval[J]. Applied Mathematics and Mechanics, 2008, 29(1): 93-103.

## 基于非线性相位恢复的X射线相位衬度断层成像算法

###### 作者简介:倪文磊(1980- ),男,山东人,博士(联系人.E-mail:evenlying@gmail.com);周铁(1963- ),男,副教授,博士生导师(E-mail:tzhou@math.pku.edu.cn).
• 中图分类号: O29；O434.19

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

• 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．
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##### 出版历程
• 收稿日期:  2007-08-03
• 修回日期:  2007-12-17
• 刊出日期:  2008-01-15

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