基于完全最小二乘原则及归一化共轭梯度法的荧光断层成像重建算法  

A Reconstruction Algorithm for Fluorescence Molecular Tomography Based on the Total Least-Squares Rule and the Normalized Conjugate Gradient Method

作　　者：尚尚[1] 白净[1] 宋小磊[1] 王洪凯[1] 

机构地区：[1]清华大学生物医学工程系,北京100084

出　　处：《航天医学与医学工程》2008年第4期338-342,共5页Space Medicine & Medical Engineering

基　　金：国家自然科学基金(30670577;60571013;60331010);清华-裕元基金;973(2006CB705700);国家863计划(2006AA020803);博士点基金

摘　　要：目的基于完全最小二乘原则,研究荧光断层成像技术。方法由漫射方程对荧光断层成像正问题建模,并使用有限元法计算出权重矩阵后,引入完全最小二乘原则,使用归一化共轭梯度法对荧光信息进行重建。结果该算法的抗噪性能优于同等情况下基于最小二乘原则的重建算法,且对于初值的稳定性较好。此外,避免了普通共轭梯度法解完全最小二乘问题时的溢出现象,使得算法的稳定性及实用性增强。结论本文所提出的算法具有较好的抗噪性、准确性及稳定性,是一种有效的荧光断层成像重建算法。Objective To find an efficient and practical reconstructionalgorithm for the fluorescence molecular tomography basing on total leastsquares rule as well as the normalized conjugate gradient method. Methods The finite element method was used to get the weighting matrix from the for- ward diffusion model. For the inverse reconstruction problem, the total least-squares rule was employed. The normalized conjugate gradient method was applied to find the fluorochrome information in the objective area. Results The simulation experiments showed that images reconstructed by the total least-squares rule were more accurate than those reconstructed by the least-squares rule un- der the same circumstances when noise existed. The presented algorithm could also give consistent results when the initial guesses varied in a wide range. Conclusion The algorithm presented in this paper offers a practical and efficient reconstruction for the fluorescence molecular tomography.

关 键 词：完全最小二乘原则 归一化共轭梯度法 荧光分子断层成像 图像重建算法 

分 类 号：R318.51[医药卫生—生物医学工程] R318.6[医药卫生—基础医学]