Generalized tomographic maps
arXiv:0802.4140 · doi:10.1103/PhysRevA.77.042115
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.
8 pages, 5 figures
References in corpus (12)
- Quantum state estimation
- Asphericity in Supernova Explosions from Late-Time Spectroscopy
- Quantum Tomography
- Experimental reconstruction of photon statistics without photon counting
- Neutrino Tomography of Gamma Ray Bursts and Massive Stellar Collapses
- Biased tomography schemes: an objective approach
- Tomograms and other transforms. A unified view
- Quorum of observables for universal quantum estimation
- Measuring the photon distribution by ON/OFF photodectors
- Radon transform on the cylinder and tomography of a particle on the circle
- Joint multipartite photon statistics by on/off detection
- Neutron wave packet tomography
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