2-DIMENSIONAL ADAPTIVE FILTERS BASED ON THE ONE-DIMENSIONAL RECURSIVELEAST-SQUARES ALGORITHM

This paper proposes a method for realizing two-dimensional (2-D) adapt ive filters by applying a one-dimensional (1-D) recursive least square s (RLS) algorithm. First, by applying a 1-D RLS algorithm along horizo ntal and vertical directions, a novel 2-D adaptive algorithm is develo ped. ft is shown that the amount of calculations in the proposed algor ithm is less than that in the misting 2-D RLS algorithm. Moreover, the convergence properties of the proposed algorithm and its relation to the conventional 2-D RLS algorithm are investigated. A method far acce lerating the rate of convergence of the algorithm using a priori estim ation error also is described. The proposed filter has good performanc e in nonstationary processes and the accuracy of convergence is better than that in the existing 2-D adaptive filters based on the least mea n square (LMS) algorithm. Therefore, the proposed filter is suitable f or processing an image with strongly nonstationary characteristics. Fi nally, the utility of the proposed filter is illustrated by applying i t to 2-D system identification under a nonstationary environment as we ll as noise reduction of an image.