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, to the point where limits on their accessibility and portability may severely restrict their usefulness for human knowledge. This often 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. In order to address this challenge, the investigator and his colleagues 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. The proposed research is expected to deliver major results for: (i) accurate representation of image and acoustic data, (ii) parsimonious representation of high dimensional data, (iii) parsimonious representation of images and volumetric objects with singularities along curves and surfaces, (iv) acceleration of scientific/engineering computations. The KDI initiative takes place at a time when intellectual and commercial life are beginning to feel the effects of a revolutionary combination: sensor ubiquity, computational ubiquity, and internet connectivity. A clear priority in all fields of commercial, engineering, and scientific endeavor must be to identify and exploit the opportunities available in this new era. The center of the effort should be the intensive development of new schemes for representing digitally acquired data, and for rapidly manipulating those representations. In fact, advances in this central area have tremendous repercussions, accelerating progress in every other area. For astronomers straining to detect faint gravitational signals coming from the farthest reaches of the universe, or looking back in time to the earliest moments after creation, searching for temperature fluctuations that would give clues about the central theories of physics; for geophysicists looking for subtle deformations in the earth's inner structure for clues about our seismic future; for engineers developing new medical imaging devices; even for Hollywood entrepreneurs wanting more realistic computer graphic simulations for mass entertainment -- data representation plays a key role. To this end, this project assembles a team of experts to address issues of developing new data representations and new methods of analysis and manipulation. The premise of this venture is that significant advances in data representation require an interdisciplinary effort, meshing the skills and knowledge of theoreticians and practitioners from varied fields of research that involve large datasets. Thus, the proposed research team consists of mathematicians, statisticians, computer scientists, and engineers with extensive skills and experience in the development and use of representations for datasets. A primary component of the project is the set of application areas in image and signal processing, large scale computation, and computer graphics. The project produces conceptual deliverables in the form of new methods for storing, compressing, denoising, and querying data. It also produces concrete deliverables in the form of algorithms and software for use in the scientific and commercial sector. The project serves as a national center for data representation. Interaction between the project and other national and international centers treating datasets is cultivated. The project also provides a national resource for theoretical advances, techniques of implementation, and software development.
