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Following the idea of including in the scattering amplitudes absorption or multiple scattering corrections, a generalization of the Frautschi-Margolis model is proposed, in which, starting from Regge poles exchange, one generates multiple scattering corrections in the form of Regge cuts. A detailed application of the model to the high energy pion-photoproduction is explained and numerical results are given both for polarized and unpolarized differential cross-sections, which are in agreement with experimental data. (Author)