Symmetries of single-slice multiple-pinhole tomographs

The singular-value decomposition (SVD) of an imaging system can be used to characterize the system. For example, because the SVD can be used to characterize the null space and range space of a system, it can be used to investigate the nature of the information a system measures and that which it does not measure. As this is the case, the SVDs of various tomographic systems have been specified and used to characterize some systems; however, specification of the SVDs of multiple-pinhole systems has not been done. We present results related to development of such a specification. A matrix operator that models a single-slice multiple-pinhole tomograph is generated via simulation, the SVD of the operator numerically obtained, and the symmetries of the system identified and correlated with symmetries of the singular vectors. Specifically, because the symmetries of the system are consistent with the structures of the dihedral group of order eight, the symmetries of the singular vectors are correlated with the irreducible representations of the dihedral group, D₄.