On the Range of the Attenuated Radon Transform in Strictly Convex Sets

Abstract

We present new necessary and sufficient conditions for a function on $\partial \Omega \times S^1$ to be in the range of the attenuated Radon transform of a sufficiently smooth function support in the convex set $\bar{\Omega }\subset {\mathbb{R}}^2$. The approach is based on an explicit Hilbert transform associated with traces of the boundary of A-analytic functions in the sense of Bukhgeim.

2 figures

References in corpus (1)

• On the range of the attenuated ray transform for unitary connections

Cited by in corpus (1)

• Inversion of the attenuated geodesic X-ray transform over functions and vector fields on simple surfaces