One-shot Training of Polynomial Cellular Neural Networks and applications in image processing

The Polynomial Cellular Neural Network (PCNN) is a fully parallel, scalable, non-linear processor that uses polynomial terms to solve non-linear problems in a lattice fashion. The parallel nature of such processor allows every neuron (or cell) to gather information from the nearby neurons and independently process the retrieved values by employing non-linear functions and synaptic weights. Nonetheless, one of the main challenges of the PCNN is the determination of the synaptic weights in order to achieve the desired behavior. In this paper, a new training method is presented, based on two fundamental concepts: the root location training method and the polynomial surfaces. The proposed training method is able to straightforwardly determine the requested synaptic weights for any outer-totallistic cellular automata behavior. In order to deliver a proof of the potential of such proposition, several image processing tasks are performed with a single layered PCNN.