Non-symmetric integral geometry: alternative reconstruction procedure with dual Radon transform

Abstract

In the note, we use the principles of non-symmetric integral geometry (non-integral geometry), related to the non-symmetric restricted integration measure, to extend the well-known relations traced from the Fourier slice theorem and the dual Radon transform. The proposed generalization is a very useful for the alternative restoration of the outset function. The latter impacts entirely on the image reconstruction process. The derived relations confirm the complexity of the inversion operator thanks for the symmetry breaking of integration measure.