ABSTRACT
This chapter defines the Radon transform of distributions using the duality relation. It discusses the spherical coordinate system and Fourier slice theorem that holds on a distribution space. Different properties of the test function spaces are provided, and the spaces of test functions are described in an explicit manner. The existence of non-zero distributions implies that the Radon transform on distributions is not uniquely defined, and non-uniqueness arises in a natural way. The chapter reviews the Range theorem for the Radon transform and provides a definition on distributions based on spherical harmonics expansion. It also discusses the dual Radon transform on distributions with regard to the classical Radon transform.
