Sparse representation of data

Advances in communication, sensing, and computational power have led to an explosion of data. The size and varied formats for these datasets challenge existing techniques for transmission, storage, querying, display, and numerical manipulation. It is thus vital to develop efficient and robust data representations that lend themselves to scientific analysis and computation. One method is to represent the data using redundant function systems. Redundant representations allow for a multitude of data decompositions. While this appears contrary to the need for efficiency, the redundancy gives the flexibility of choosing `best representations' from a unified family of representers and thereby provides efficiency and robustness. In this project sparse representation of data using redundant systems is studied both from a theoretical and a practical point of view.