Singularities of the Radon transform

Abstract

Singularities of the Radon transform of a piecewise smooth function f ( x ) f(x) , x ∈ R n x \in {R^n} , n ≥ 2 n \geq 2 , are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of f ( x ) f(x) are calculated by applying the Legendre transform to the functions, which appear in the equations of the discontinuity surfaces of the Radon transform of f ( x ) f(x) ; examples are given. Numerical aspects of the problem of finding discontinuities of f ( x ) f(x) , given the discontinuities of its Radon transform, are discussed.