CIF: Small: Dictionary Learning for Compressed Sensing

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

The digital information revolution relies on the sensing and conversion of real-life signals such as speech, music, images and movies to numbers that can be manipulated by computers. Compressed sensing is a recent breakthrough in mathematics that enables to do this sensing and conversion more efficiently and reliably than ever thought possible. Key to this, is the availability of efficient dictionaries that enable very compact representation of natural signals. While dictionaries have been developed from mathematical principles, a recent discovery is that their efficiency can be greatly enhanced, if the dictionary itself is learned from examples of the data. Because compressive sensing depends critically on the interaction of the dictionary with the sensing mechanism, joint learning of the two from the data itself is expected to provide the greatest benefits. However, to date there have been only a handful of heuristic attempts in this direction. The investigator is developing the first systematic theory for dictionary learning, and for joint learning of dictionaries and sensing mechanism. He will demonstrate the theory and algorithms on real sensing applications, and in particular on challenging medical diagnostic applications. The specific goals of this project are to develop theory and algorithms with performance guarantees for (i) learning dictionaries for sparse signal representation for compressive sensing; (ii) joint learning of dictionary and the sensing operators optimum for compressive sensing; and to demonstrate the theory and algorithms on challenging magnetic resonance imaging (MRI) and computerized tomography (CT) applications. Ultimately, this research may lead to MRI and CT techniques for improved imaging of the beating heart or brain function from less data in less time, improving health care and reducing its cost.