Image compression with learnt tree-structured dictionaries

In the present paper we propose a new framework for the construction of meaningful dictionaries for sparse representation of signals. The dictionary approach to coding and compression proves very attractive since decomposing a signal over a redundant set of basis functions allows a parsimonious representation of information. This interest is witnessed by numerous research efforts that have been done in the last years to develop efficient algorithm for the decomposition of signals over redundant sets of functions. However, the effectiveness of such methods strongly depends on the dictionary and on its structure. In this work, we develop a method to learn overcomplete sets of functions from real-world signals. This technique allows the design of dictionaries that can be adapted to a specific class of signals. The found functions are stored in a tree structure. This data structure is used by a Tree-Based Pursuit algorithm to generate sparse approximations of natural signals. Finally, the proposed method is considered in the context of image compression. Results show that the learning Tree-Based approach outperforms state-of-the-art coding technique.