A general definition for a symmetry group of an imaging system is given. A key requirement is that the operators that represent the symmetries in data space are conformal. The result is that the space of consistency conditions is invariant under the action of the given symmetry group. Via the theory of group representations, this fact provides information about the possible forms that these consistency conditions can take. The theory is illustrated by example for the 2D and 3D Radon transforms, the cone-beam transform on a circular orbit and the 2D attenuated Radon transform.
ASJC Scopus subject areas
- Radiological and Ultrasound Technology
- Radiology Nuclear Medicine and imaging