A Bayesian approach to video expansions on parametric over-complete 2-D dictionaries

In this work, we explore a framework for the sparse representation of video sequences by means of spatio-temporal functions able to exploit the 2D nature of images and the temporal smoothness associated to object trajectories. Decomposition over redundant dictionaries formed by 2D functions capable to exploit image geometry, has shown to be well adapted for efficient sparse image approximations. Video representation by means of temporally evolving sets of such 2D functions seems thus a natural extension toward video approximation techniques. In the present paper we study the deformation of a geometry oriented image expansion based on matching pursuits (MP) (P. Vandergheynst and P. Frossard, May 2001), to obtain a parametric representation of frames transformation through time. We consider a modified MP approach based on a Bayesian decision criteria to deform geometrical primitives in a predictive fashion from frame to frame. Indeed, since motion stability is not guaranteed using a pure MP, a Bayesian framework is introduced to regularize motion among expansion terms of frames representations.