The Studies About The Singular Detection And Inversion Of Radon Transform

This paper studies the singularity of Radon transform and the inversion of Radon transform for a class of piecewise smooth function. we can't obtain the precise inversion. of the original function when we make the radon transform inversion by using of the convolution-projection method. Frist,we study separately the singular inversion of Radon transform. We give the relation between the singularity of a class of piecewise functions and the singularity of its radon transform when the singularity occurrs in the boarder and internal of funcition's support. In addition,we have also make use of the wavelet transform which have nature of the singularity detection,namely, Namely, we can detect the positions of the singular points of the function by tracking the the maxima modulus of the wavelet transform in the small-scale range . Also we can inverse the similarity of the original function by using of the dual nature of Legendre transform. We find that we can get a great error if the derivative of the singular curve is too big when we make the numerical inversion,so we make a limit for the interval space of the variable to separate the singular curves of the radon transform. Therefore we can achieve the the precise inversion of the singularity of the original function.