Uniqueness characteristics of the 2-D IIR mean squared error minimization

Several different two-dimensional adaptive filter structures and algorithms have been developed, the most recent of which is a 2D IIR adaptive filter. Two-dimensional IIR adaptive filters can be used in a variety of image and video processing applications. Of primary concern with IIR adaptive filters, whether 1D or 2D, is the possible existence of multiple stationary points on the mean-squared error surface. Gradient based adaptive algorithms can get stuck at suboptimal local minima, rendering themselves less effective. Results show that the 2D IIR mean-squared-error performance surface characteristics are similar to those of the 1D IIR adaptive filter with respect to unimodality of the error surface. The authors explore the mathematical characteristics of the 2D IIR MSE minimization problem. Some simple special cases are examined, and experimental evidence is discussed.