Non-separable non-linear decompositions with applications to image compression

Linear separable multi-resolution decompositions are extensively used in many signal processing applications. Recently, there has been a growing interest in both non-linear and non-separable decompositions, due to their increased flexibility when compared to either linear or separable ones. Of special interest is the case where the decompositions are both non-linear and non-separable. However up to now, there are no general tools for the design of such decompositions. This work suggests an heuristic to design maximally-decimated non-separable non-linear decompositions. First, a particular case of a non-separable structure found in the literature are presented. Then non-linear operators suitable for use in that are listed. The design strategy is described and preliminary non-linear non-separable designs are generated. The image coding performance of these decompositions is very close to the one achievable with the best known linear filter banks. This suggests that the proposed heuristic is an effective tool for the design of non-linear decompositions, which opens exciting research possibilities.