Simultaneous approximation of images applications to image and video compression

Abstract

Given a set of images we propose an algorithm that approximates all images simultaneously. The algorithm finds the best common partition of the images' domain at each step, this is accomplished by maximizing an appropriate inner product. The algorithm is a pursuit algorithm constrained to build a tree, the optimization is done over a large dictionary of wavelet-like functions. The approximations are given by vector valued discrete martingales that converge to the input set of images. Several computational and mathematical techniques are developed in order to encode the information needed for the reconstruction. Properties of the algorithm are illustrated through many examples, comparisons with JPEG2000 and MPEG4-3 are also provided.