ON THE RECURSIVE COMPUTATION OF INTERPOLATORS WITH NONRECTANGULAR MASKS

An algorithm is presented for the recursive computation of finite-orde r interpolators and predictors for scalar random processes on multidim ensional parameter sets. The algorithm is able to achieve computationa l 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 o f the interpolation filter and the low displacement rank properties of the correlation matrix, The paper presents the method for step-by-ste p growth of the interpolation support and shows that an interpolation filter can be constructed from the interpolator of the previous step a long with certain interpolators corresponding to the boundary points o f the filter support in the previous step. When restricted to rectangu larly shaped masks, the algorithm has the same order of complexity as previous algorithms for solving Toeplitz-block Toeplitz systems.