Optimal reduced pyramid interpolation for lossless and progressive image coding

Reduced pyramids, including in particular pyramids without analysis filters are known to produce excellent results when used for lossless signal and image compression. The present paper presents a methodology for the optimal construction of such pyramids by selecting the interpolation synthesis post-filters so as to minimize the error variance at each level of the pyramid. This establishes optimally efficient interpolative pyramidal lossless compression. It also has the added advantage of producing lossy replicas of the original which, at lower resolutions retain as much similarity to the original as possible. The general optimization methodology is developed first, for a general family of reduced pyramids. Subsequently, this is applied to the optimization of pyramids in this family formed using 2D quincunx sampling matrices. Optimal versions of these techniques are determined for 2D images characterized by separable or isotropic correlation functions. The advantages of the developed methods are demonstrated by experimental evaluation