Exponential nonlinear Volterra filters for contrast sharpening in noisy images

This paper presents a preliminary study of a new class of nonlinear (Volterra) filters which reduce the noise in an image while simultaneously enhancing the contrast. The design of these filters draws heavily from the theory of generalized Fock (GF) spaces of Volterra series. The structure of these filters is obtained by an orthogonal projection in a GF space under the data constraints. As a consequence, even though this structure embodies an infinite Volterra series, it is represented in a closed form as a linear combination of exponentials, the exponents of which are linear functions of the input image vector.