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When a random noise is superposed on a non-Gaussian signal with an abruptly changing component, as in the ease of the image signal, it is impossible for the conventional linear filter to eliminate the noise effectively. This is one of the cases where the nonlinear filter should be applied. This paper proposes a nonlinear digital filter based on the layered neural network, including the optimization of the nonlinear function. The proposed filter can effectively eliminate the noise by utilizing the nonlinearity of the layered neural network and its learning function. Another point is that the performance can be improved by the piecewise-linear approximation of the nonlinear function and the automatic design of the optimal nonlinear function. The effectiveness of the proposed filter is demonstrated by eliminating the noise from the two-dimensional image signal. [ABSTRACT FROM AUTHOR]