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Universal inverse Radon transforms: Inhomogeneity, angular restrictions and boundary
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An alternative method to invert the Radon transforms without the use of Courant-Hilbert's identities has been proposed and developed independently from the space dimension. For the universal representation of inverse Radon transform, we study the consequences of inhomogeneity of outset function without the restrictions on the angular Radon coordinates. We show that this inhomogeneity yields a natural evidence for the presence of the extra contributions in the case of the full angular region. In addition, if the outset function is well-localized in the space, we demonstrate that the corresponding boundary conditions and the angular restrictions should be applied for both the direct and inverse Radon transforms. Besides, we relate the angular restrictions on the Radon variable to the boundary exclusion of outset function and its Radon image.
Forward citations
Cited by 2 Pith papers
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Non-integral geometry: additional term $f_A$ as a regularizing term
The additional term f_A in the universal inverse Radon transform removes complex singularities that arise for non-symmetric supports, provided certain log-branch parameters are chosen appropriately.
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Complexity of Radon transforms
The paper argues that inverse Radon reconstruction requires complex direct Radon images and proposes a partial Fourier transform trick plus a claimed holonomy effect to generate that complexity.
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