Design of 2-D recursive digital filters in the spatial domain

A class of least-squares algorithms for designing two-dimensional digital filters from space-domain data is presented. The proposed algorithms iteratively estimate the filter coefficients by minimizing the true squared error between the given and the estimated space-domain responses. The algorithms are essentially generalizations of the optimal 1-D design algorithm given by A.G. Evans and R. Fischl (1973). The error criterion is simultaneously optimized with respect to the coefficients in both dimensions. Design algorithms are given for filters with separable and irreducible numerator/denominator polynomials and also for mixed structures. The effectiveness of the algorithms is illustrated with several simulation examples.<>