Speaker: Glenn Easley, University of Maryland

Title: Beyond Wavelets: The Shearlet Transform

Abstract: As our society has become increasingly dependent on storing and manipulating data like images or maps in a digital medium, techniques to compress such data are paramount. Methods based on wavelets have emerged in the last 20 years as some of the most successful approaches to represent such data efficiently. For example, wavelets are used to compress the FBI's fingerprint database and in the new image compression scheme JPEG2000. Despite wavelets' remarkable success, there is still room for improvement in dimensions greater than one. For instance, the wavelet transform is known to be suboptimal when dealing with a certain class of images, e.g. images described as C^2 functions away from piecewise C^2 curves. In the past seven years, researchers have tried to go beyond wavelets by developing transforms that exploit the geometric regularities of multidimensional objects. In this talk, we develop a new geometric transform, called the shearlet transform, designed to handle such images optimally. We conclude with several examples indicating that shearlets are the latest competitor to beat for representing images sparsely.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491