Extensions of 2-D iterative digital filters

A 2-D digital filter with a rational frequency response, as previously shown, can be implemented with an infinite sequence of finite-extent impulse response (FIR) filtering operations, provided a certain convergence criterion is satisfied. In this paper, the iterative procedure is generalized so that the convergence requirement is always met, thus allowing an iterative implementation of any stable rational 2-D infinite impulse response filter. The modification requires the pre-filtering of the numerator and denominator polynomials of the rational frequency response and a relaxed formulation of the original iteration. A frequency-varying relaxation parameter is considered for increasing the rate of convergence over the entire frequency band of interest. Tradeoffs between the size of the 2-D FIR filters used within the iteration and convergence rates are demonstrated by applying the relaxed form of the iteration to the problem of image deblurring.