Singularities of the Radon transform
Alexander G. Ramm, Alexander I. Zaslavsky
Abstract
Singularities of the Radon transform of a piecewise smooth function f(x), x∈ Rn, n≥ 2, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of 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); examples are given. Numerical aspects of the problem of finding discontinuities of f(x), given the discontinuities of its Radon transform, are discussed.
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