A design method of two-dimensional recursive digital filter by using Laguerre functions

Because of the difficulty in factorizing two-variable functions, few papers have reported on the design of two-dimensional recursive digital filters via a cascade connection of two-dimensional filters obtained by the coordinate rotation of one-dimensional filters or by nonlinear programming. This paper proposes a systematic method of the transfer function whose impulse response is the sampled value of a given image by use of Laguerre function. Similar to the case of nonrecursive filters, the transfer function of recursive filters can be expressed in a form of the sum of the products of one-variable functions and can be realized in a combination of cascade and parallel structures. The coefficients of the transfer function are calculated numerically by approximating an image by a two-variable polynomial.