A 2-D Adaptive Volterra Filter Based on LMS Method

The Volterra filter is a nonlinear filter presented by the Volterra series expansion which is well known as a generalization of the Taylor series expansion. From a practical point of view, a number of applications have been limitted to using second-order Volterra filters, because of the computational complexity that exponentially increases with the Volterra filter order. On the other hand, few researchers have attempted to design two-dimensional (2-D) Volterra filters in 2-D signal fields. The purpose of this paper is to present a 2-D Volterra filter which can deal with 2-D signal such as image signal and determine the optimum Volterra kernel in the same manner as the approach for I-D case, based on the assumption that the input field is Gaussian. Also, 2-D adaptive Volterra filter based on LMS algolithm is designed, and then, for 2-D system identification, the effectiveness of the proposed adaptive filter is evaluated using digital computer simulations