Stable nonlinear recursive filters for edge enhancing noise smoothing of images

Stability conditions for nonlinear recursive filters of the form y(n)=f(x(n, y(n-1)), y(n-2), . . ., y(n-N)) where f is equal to a linear combination of x(n), y(n-i), i=1, 2, . . ., N with nonconstant coefficients. A specific scheme is proposed for simultaneous noise smoothing and edge sharpening of images. The problem of distortion similar to that due to the nonlinear phase of linear recursive filters is solved by incorporating multidirectional filtering methods. Results of using this nonlinear recursive image filter show that the quality of image is not only restored but also improved in the case of low- to medium-variance noise.<>