What’s New

Bregman Iteration and Applications to Imaging and Sparse Representation

Posted on 1/9/09 in Research Articles

A breakthrough in the sparse representation of data was made in the Fall of 2004 by David Donoho and by Emmanuel Candes and Terence Tao, in part at IPAM’s Multiscale Geometry and Analysis program. Their important results reduce a computationally difficult problem to an easily […]

read full article
Magnetic Resonance Imaging of a sharp disk, using a traditional method (left) and a new method based on Compressed Sensing and Bregman iteration (right), from work of T. Goldstein.

Describing protein motions with nonlinear dimensionality reduction

Posted on 7/18/08 in Research Articles

Twenty years ago, commenting on macromolecular dynamics, Francis Crick wrote that “what seems to physicists a hopelessly complicated process may have been what Nature found simplest.” Indeed, if one uses molecular dynamics simulations (that follow the molecular motion of biological systems in the high dimensional […]

read full article
Image courtesy of Mark Moll, Payel Das and Hernan Stamati (Rice University, Houston, Texas).

Better Seismic Imaging

Posted on 2/21/08 in Research Articles

The economic value to the oil industry of 3D seismic imaging is approximately $11 billion annually. How accurately seismic imaging can be done depends on both the quality of the sensing equipment, but also very much on the effectiveness of the mathematical algorithms that are […]

read full article
seismic imaging-2

Sparse Representations

Posted on 11/17/07 in Research Articles

What do researchers studying infrared spectroscopy, seismic imaging, error correcting codes, and MRI’s have in common? They all can get better results if they have the right math. Fourier analysis, discovered in analyzing the flow of heat, revolutionized how mathematics is used in a variety […]

read full article
sparse reps