Neural network approach to 2D Kalman filtering in image processing

The authors deal with the problem of Kalman filtering of 2D systems (images) with randomly disturbed state and output described by a general model of 2D systems given by J. Kurek (1985). Kalman filter equations are derived for a reduced version of the 2D system model, and the resulting state estimate is expressed in terms of the original 2D system. A neural network for computing the filter gain is proposed. The Riccati equation is reduced to a series of linear Lyapunov equations following the method of D.L. Kleinman (1968). The neural network was applied to obtain the solution of the Lyapunov equation that in turn gave the solution of the Riccati equation and the Kalman filter algorithm. The results were obtained by computer simulation of the proposed neural network.