Advances in communication, sensing, and computational power have led to an explosion of data. The usefulness of this resource for human knowledge is determined by its accessibility and portability. The size and varied formats for these datasets challenge existing techniques for transmission, storage, querying, display, and numerical manipulation. This leads to the paradoxical situation where experiments or numerical computations produce rich, exquisitely detailed information, for which, at this point, no adequate analysis tools exist. The solution to this dilemma is the development of efficient and robust data representations that lend themselves to scientific analysis and computation.
The research mission of the Wavelet IDR Center is to develop a new technology for data representation based on the two basic principles of multiscale decompositions and redundant representations. Multiscale decompositions arrange data into strata reflecting their relative importance. This allows for rapid access to good coarse resolution of the data while retaining the flexibility for increasingly fine representations. Redundant representations allow for a multitude of data decompositions. While this on the surface 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.
A premise of the research mission is that significant advances in data representation require an interdisciplinary effort. The research team of Wavelet IDR Center is composed of leaders from the field of Computational Harmonic Analysis along with experts in important application domains for data representation (computer graphics, network communication, large scale computation). The general aim is to develop a new generation of multiscale methods for data representation: significantly better representations for data, fast algorithms for obtaining those representations, and new ways to process and analyze data based on those representations. The coordinating structure behind this effort is the division of research activities into subteams.
