Joint sublattice selection and prefilter design for the optimal decimation of 2-D digital signals

摘要

Signal decimation aimed at optimal spectral packing has a variety of applications in areas ranging from array processing to image processing. The authors propose and discuss a new method for determining the decimation grid and prefilter that best fit the spectral extension of any 2-D signal defined on an arbitrary sampling lattice. The method first quantifies the spectral anisotropy through the determination of the principal axes of the power spectrum, then it selects among all possible decimation grids those that are compatible with the spectral extension shaped on the ‘inertia' ellipse. Finally, for each of them it geometrically constructs the ideal prefilter whose convex passband best encircles this spectral extension. A final selection is thus made among the available sublattice/prefilter pairs according to some specific criterion. The method, implemented in a fully automatic computer procedure, has been tested over several digital images to evaluate its performance in terms of the impact of the spectral truncation on the overall quality of the reconstructed images.