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

Quantum tomography with wavelet transform in Banach space on Homogeneous space