Jv. Krogmeier, ON THE RECURSIVE COMPUTATION OF INTERPOLATORS WITH NONRECTANGULAR MASKS, IEEE transactions on signal processing, 44(5), 1996, pp. 1072-1079
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.