Adaptive Kriging Filters for Multidimensional Signal Processing

The Wiener filter is the well-known solution for linear minimum mean square error (LMMSE) signal estimation. This filter assumes the mean to be known and usually constant. On the other hand, the Kriging filter is an incremental theory, developed within the Geostatistical community, with respect to that of Wiener filters. The extension relies on adopting a parametric model for the mean (usually a polynomial). The goal of this paper is twofold. First it is intended as a comprehensive treatment of the Kriging approach from a Signal Processing perspective, with previous uses of Kriging in Signal Processing being extended. Second, we are deriving a general methodology for FIR filter design, including any situation where an optimal FIR estimator from possibly incomplete and/or noisy data is needed. Selected examples illustrate the performance of the method on some common Image Processing problems (interpolation, approximation and filtering).