Integral transforms between tomogram and quasi-probability functions based on quantizer-dequantizer operators formalism

An application of a quantizer-dequantizer method as a unifying description for representations of states in quantum mechanics is considered. Well-known quasi-distributions and tomograms are rewritten in terms of the dequantizer and quantizer operators. Using this description of the tomographic probability function and its symbol, we construct the invertible integral transforms between the tomogram and the quasi-probability distributions such as Wigner, Kirkwood-Rihaczek, Choi-Williams, P- and Q-functions, and others.