Least squares inverse polynomials and a proof of practical BIBO stability of n-D digital filters

The problem of stabilizing unstable n-dimensional practical digital filters is discussed, where only one of the independent variables of the n-D signal is temporal and the other variables are spatial. The double-least-squares inverse method is used to stabilize such practical filters. It is proved that the least-squares inverse of the denominator polynomial of a practical n -D digital filter is always stable in the practical and less restrictive sense