一维小波检测和反演二维空间中Radon变换的奇性

Detection and Inversion for Singularitie of Radon Transform in Two-dimensional Space

在二维空间中,基于Radon变换的理论,以小波变换作为工具,及利用此分片光滑函数积分线旋转变化时得到的、Ra-don变换的奇性传播规律,得到Radon变换的奇性反演公式。检测分片光滑函数Radon变换的奇性曲线,并根据原函数与其Radon变换奇性的关系;利用Legendre变换的对合性质来反演出原函数的奇性曲线。

In two-dimensional space, the singdar curve of the Radon transform is detected to a piecewhse smooth function by the wavelet transform as a tool, based on the theory of Radon transform and the relation between the singularties of a class fufnction and the singulav curve of the original function using of the properity of the Legendre transform and the relation of the original function and the singularity of the Radon transform.