Joint automatic design of prefilter and decimation grid for the reduction of spectral redundancy in 2D digital signals

In this paper we propose and discuss a new technique for reducing the spectral redundancy of 2D digital signals through decimation on an arbitrary sublattice. Starting from a second-order analysis of the signal's spectral extension, the method automatically selects a decimation grid that minimizes the overlap between spectral replicas and defines an ideal hexagonal prefilter that maximizes the spectral energy to be preserved. Furthermore, the method automatically designs the hexagonal prefilter through a modified version of the frequency transformation method. In particular, it geometrically designs the transformation map in such a way to fit the prefilter's passband. The method has been tested over a variety of 2D test signals (non-synthetic digital images) in order to evaluate the performance of the method in terms of the impact of the spectral truncation on the overall quality of the reconstructed signal.