Mathematical models of neural networks were centered at the point of nonlinear inertial transformations which seemed to be a crucial point of any signal processing. The commonly used way to deal with these transformations is to represent them by functional series. A method was proposed to approximate the kernels of integral operators appropriate to Zadeh's series by simple neural network operators, which include sample operations with variable time spacing, integration and comparison with variable thresholds.
( V.Gusev, V.Chihman - Neural networks in processing and efferent control of sensory information. Abstracts of the 4-th IBRO World Congress of Neuroscience, Kyoto, Japan, 1995, N 206.)An another extension of the proposed approach was an attempt to consider only multiplicative group of signal transformations and apply them to process the images, considered always as a source of mono-signed data. ( V.Gusev, V.Chihman - Multiplicative neural networks in image processing. Abstracts of the IS&T/SPIE Symposium on Electronic Imaging: Science and Technology - Applications of Artificial Neural Networks in Image Processing, 27 Jan.-2 Feb. 1996, San Jose, California, USA, Abstract ( 2664-25 ).)