  The intimate connection between the Banach space wavelet reconstruction
method on homogeneous spaces with both singular and nonsingular vacuum vectors,
and some of well known quantum tomographies, such as: Moyal-representation for
a spin, discrete phase space tomography, tomography of a free particle,
Homodyne tomography, phase space tomography and SU(1,1) tomography is
explained. Also both the atomic decomposition and banach frame nature of these
quantum tomographic examples is explained in details. Finally the connection
between the wavelet formalism on Banach space and Q-function is discussed.
