A structured matrix approach for spatial-domain approximation of 2-D IIR filters

This work addresses least-squares (LS) approximation of a prescribed spatial response by a quarter-plane 2-D IIR filter. Using structured matrix representation it is shown that the spatial domain error vector between the desired and estimated responses is linearly related to the numerator coefficients and nonlinearly related to the denominator coefficients. The numerator and denominator estimation problems are theoretically decoupled without affecting the optimality properties. The decoupled denominator criterion possesses a quasi-quadratic form and its optimization is computationally efficient requiring very few iterations, The numerator is estimated linearly in a single step. Effectiveness of the algorithm is demonstrated with several examples.