Program on Inverse Problems and Imaging at the Fields Institute in 2012

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

This project will support research and educational activities as part of the Thematic Program on Inverse Problems and Imaging at the Fields Institute in 2012. The organizers aim to create an environment conducive to collaborative research by combining the particiapnts' high-level expertise from Partial Differential Equations, Nonlinear Variational Methods, Differential Geometry, Regularization Theory and Numerical Analysis. Techniques initially developed in image processing or in microlocal analysis will be extended to treat novel hybrid inverse problems. Modern faster and more accurate optimization techniques for recovering data from undersampled measurements will be explored. Nonlocal methods have been recently proven to be the most efficient techniques in image denoising and image regularization. Current and future directions for solving a large range of inverse problems by nonlocal methods and their computational challenges will be studied. By integrating research and education, the organizers will introduce next generation researchers in Medical Imaging to the recent important and deep mathematical advances in the field. Numerous lectures, graduate and short courses will be given by leading researchers in the fields of inverse problems and imaging. These problems have important applications in medical imaging, geophysical prospecting and nondestructive testing. Graduate and postdoctoral students will greatly benefit from being exposed to these most active areas of research in mathematics today. They will also be exposed to interdisciplinary research mixing theoretical advances with up to date applied issues. Women and underrepresented groups will be given the opportunity to actively participate in the program as organizers, speakers, and regular participants. Teams of graduate students will be offered a summer research experience on concrete problems in medical imaging.