Tree structured pursuit for simultaneous image approximation

The paper introduces an adapted orthonormal system to approximate a collection of given images. The associated construction is performed by a pursuit algorithm constrained to build a tree; the pursuit maximization is performed over a large dictionary of Haar wavelet-like functions. The approximations are given by vector valued discrete martingales that converge to the vector of input images. A natural application for our construction is the case when the set of images is given by a sequence of video frames. We describe the trade off between the size of the input set and the quality of the approximation and provide examples and comparisons.