Generalized tomographic maps

Details Generalized tomographic maps Generalized tomographic maps

2008-02-28

arxiv.org/abs/0802.4140v1

Physical Review A 77, 042115 (2008)

Physics

Mathematical Physics

8 pages, 5 figures

Scientific paper

10.1103/PhysRevA.77.042115

We introduce several possible generalizations of tomography for quadratic surfaces. We analyze different types of elliptic, hyperbolic and hybrid tomograms. In all cases it is possible to consistently define the inverse tomographic map. We find two different ways of introducing tomographic sections. The first method operates by deformations of the standard Radon transform. The second method proceeds by shifting a given quadric pattern. The most general tomographic transformation can be defined in terms of marginals over surfaces generated by deformations of complete families of hyperplanes or quadrics. We discuss practical and conceptual perspectives and possible applications.

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