On the recursive computation of interpolators with nonrectangular masks

An algorithm is presented for the recursive computation of finite-order interpolators and predictors for scalar random processes on multidimensional parameter sets. The algorithm is able to achieve computational savings even for interpolation filters with nonrectangularly shaped support because it avoids direct exploitation of Toeplitz structure in the normal equations by using the displacement invariance structure of the interpolation filter and the low displacement rank properties of the correlation matrix. The paper presents the method for step-by-step growth of the interpolation support and shows that an interpolation filter can be constructed from the interpolator of the previous step along with certain interpolators corresponding to the boundary points of the filter support in the previous step. When restricted to rectangularly shaped masks, the algorithm has the same order of complexity as previous algorithms for solving Toeplitz-block Toeplitz systems.