The K-SVD: Design of Dictionaries for Sparse and Redundant Representation of Signals
August 2nd, 2005
SPIE meeting, San-Diego, CA. Invited Talk.

In recent years there is a growing interest in the study of sparse representation for signals. Using an over-complete dictionary that contains prototype signal-atoms, signals are described as sparse linear combinations of these atoms. Recent activity in this field concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting pre-specified transforms, or by adapting the dictionary to a set of training signals. Both these techniques have been considered in recent years, however this topic is largely still open. In this presentation we address the latter problem of designing dictionaries, and introduce the K-SVD algorithm for this task. We show how this algorithm could be interpreted as a generalization of the K-Means clustering process, and demonstrate its behavior in both synthetic tests and in applications on real data. The accompanying paper also describes its generalization to non-negative matrix factorization problem that suits signals generated under an additive model with positive atoms.

Joint work with Michal Aharon and Alfred M. Bruckstein.