Applied Computational Mathematics Division


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Sparse Representations and High Dimensional Geometry: What's the Excitement?

Bradley K. Alpert
Information Technology Laboratory, Mathematical and Computational Sciences Division

Tuesday, December 5, 2006 15:00-16:00,
Building 101, Lecture Room B
Gaithersburg
Tuesday, December 5, 2006 13:00-14:00,
Room 4511
Boulder

Abstract: Can one reliably construct an N-pixel image from N^1/4 measurements? Can one transmit a message despite jamming by a clever adversary who manages to corrupt almost 1/3 of the bits? For several years computational experiments and practice have supported the use of the L1 norm for fitting models to measurements in certain applications. In the past two years, theory has begun to catch up to practice, to remove some of the mystery of these computations, and to open many new applications. Emmanuel Candes, David Donoho, Anna Gilbert, Ron DeVore, their collaborators, and a growing list of other researchers have provided both algorithms and theorems to suggest a new approach to information acquisition and processing, one in which extremely underdetermined problems can be solved well by finding sparse (or sparsest) solutions. This talk aims to introduce these ideas and methods. In addition, results of some numerical experiments to infer discontinuous images from truncated Fourier-domain data will be presented.

Speaker Bio: Brad Alpert is a staff member of NIST's Mathematical and Computational Sciences Division, which he joined fifteen years ago. He received BS and MS degrees in Mathematics from the University of Illinois at Urbana-Champaign and the University of Chicago, respectively. He received a PhD in Computer Science from Yale University in 1990. He has held positions as a Hans Lewy Postdoctoral Fellow at the University of California, Berkeley, and more recently as a Visiting Researcher at Courant Institute in New York. His research interests include the numerical solution of integral equations, high-order quadratures, the fast multipole method, wavelets, special functions, computational electromagnetics, and inverse scattering. He is currently an Associate Editor of the SIAM Journal on Scientific Computing and received the Arthur S. Flemming award in 2006.

Presentation Slides: PDF

Contact: P. M. Ketcham

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.