  Quantum tomography for continuous variables is based on the symplectic
transformation group acting in the phase space. A particular case of symplectic
tomography is optical tomography related to the action of a special orthogonal
group. In the tomographic description of spin states, the connection between
special unitary and special orthogonal groups is used. We analyze the
representation for spin tomography using the Cayley-Klein parameters and
discuss an analog of symplectic tomography for discrete variables. We propose a
representation for tomograms of discrete variables through quaternions and
employ the qubit-state tomogram to illustrate the method elaborated.
