Radon变换方法重建高维波动方程声速系数  

SONIC SPEED RECONSTRUCTION FOR WAVE EQUATION IN HIGH-DIMENSION SPACE BY RADON TRANSFORM

作　　者：李晓峰[1] 朱本仁[1] 

机构地区：[1]山东大学数学与系统科学学院,济南250100

出　　处：《山东大学学报（理学版）》2002年第1期5-11,共7页Journal of Shandong University(Natural Science)

摘　　要：研究了高维波动方程的反问题 ,根据奇性解的演化去求声速的Radon变换 ,将反问题的解转化为Radon反变换 ,而Radon反变换能够只根据外部测量数据重建内部截面图像 .The inverse problem of wave equation in high-dimension space is studied.Instead of the traditional inverse scattering method,the Radon transform of sonic speed is obtained according to the properties of the singular solution,then solving the inverse problem is converted to Radon inverse transform.Radon inverse transform can reconstruct the cross section image even though only the outside data is measured.Some instances computed prove the validity of this method.

关 键 词：声速系数 RADON变换 高维波动方程 反问题 声速反演 Radon反变换 奇性解 数学物理问题 

分 类 号：O411.1[理学—理论物理]