Recurrent neural networks as approximators of non-linear filters operators

Abstract

In cases that the mathematical model of a device is complicated or it can not be constructed because of the absence of sufficient information about a researched object, the approach based on the description of unique relationship between the sets of input and output signals is used. The point is the approximation of a non-linear operator, establishing the unique input-output mapping, by mathematical constructions (multidimensional polynomials, regression models, neural networks). Demand to reach the high accuracy of approximation often arises in practice. Recurrent neural networks possessing the properties of dynamics and nonlinearity are considered as mathematical models within the framework of the input-output approach. The non-linear filters synthesis is the constructing of mathematical models using the available sets of input and output signals. Non-linear filters serve for cancelling non-Gaussian noise from distorted signals. As an example, images distorted by the impulse noise is recovered with the help of non-linear filtering performed by different kinds of neural networks.