Image compression with learnt tree-structured dictionaries

• Published in: IEEE 6th Workshop on Multimedia Signal Processing, 2004 pp. 35 - 38
• Main Authors: Monaci, G., Jost, P., Vandergheynst, P.
• Format: Conference Proceeding
• Language: English
• Published: Piscataway NJ IEEE 2004
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Dictionaries; Exact sciences and technology; Image coding; Matching pursuit algorithms; Paper technology; Pattern recognition. Digital image processing. Computational geometry; Pursuit algorithms; Signal design; Signal generators; Signal processing; Signal processing algorithms; Tree data structures; Multimedia; Dictionaries; Tree structured method; Real function; Redundancy; Data compression; Sparse representation; Image compression; Approximation algorithm; Function representation; Signal representation; Data structure
• ISBN: 0780385780; 9780780385788
• DOI: 10.1109/MMSP.2004.1436409

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 an 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.