Generalized tomographic maps
Mathematical Physics
2009-11-13 v1 math.MP
Quantum Physics
Abstract
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.
Cite
@article{arxiv.0802.4140,
title = {Generalized tomographic maps},
author = {M. Asorey and P. Facchi and V. I. Man'ko and G. Marmo and S. Pascazio and E. C. G. Sudarshan},
journal= {arXiv preprint arXiv:0802.4140},
year = {2009}
}
Comments
8 pages, 5 figures