A new 2D adaptive nonlinear filter based on the Lyapunov stability theory

In this paper, a new 2D adaptive nonlinear filter is proposed. Its stability is guaranteed using Lyapunov stability theory. This algorithm profits of the matrix structure of the window (mask), used to define the 2D signal as a nonlinear model of exponential form. This nonlinear exponential model may be easily expanded in a Taylor series leading a higher order polynomial filter. Using the Lyapunov stability theory, it is shown that the new algorithm is independent of the stochastic character of the input signal. Simulation results highlight the efficiency of the new algorithm.