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It is shown how nonlinearly mixed signals can be retrieved uniquely by using a novel approach based on signal restoration methodology rather than the conventional technique of mere signal separation. A new mathematical model of the nonlinear mixing system has been developed culminating in the formulation of a stable unique inverse solution, which has an identical structure to the multilayer neural network. In addition, it is shown how the optimum framework for the nonlinear demixing system can be obtained directly from the derived mixing model. It is further shown how the proposed schemes using the multilayer polynomial neural network (PNN) can be utilised to acquire the desired solution. Moreover, the corresponding learning algorithm based on the generalised stochastic gradient descent method combined with a modified genetic algorithm (GA) has been developed to yield a novel and more effective approach in updating the parameters of the PNN. Both synthetic and real-time simulations have been conducted to verify the efficacy of each proposed scheme.