Computational Approaches for Large Scale Inverse Problems for Image Reconstruction - James Nagy, Emory

James G. Nagy
Emory University
http://www.mathcs.emory.edu/~nagy/
Date: Thurs., Dec. 1, 2011

Title: Computational Approaches for Large Scale Inverse Problems for Image Reconstruction

ABSTRACT: The problem of reconstructing an image of an unknown object from measured data arises in many applications, including microscopy, medicine, and astronomy. Image reconstruction typically requires solving a large scale ill-posed inverse problem, which is very sensitive to perturbations, such as noise, in the data. To compute a physically reliable approximation from given noisy data, it is necessary to incorporate appropriate regularization (i.e., stabilization) into the mathematical model. Computational approaches to solve the regularized problem require effective numerical optimization schemes, efficient large scale matrix computations, and high performance computing strategies. In this talk we discuss the challenges of computing approximations of large scale inverse problems, how to analyze the challenges using the singular value decomposition, and how to efficiently implement the ideas with iterative methods on realistic problems. Several examples will be used to illustrate the key ideas. New developments in this field often depend on the particular application, and we describe some of our recent contributions in astronomical and medical imaging.

BIO: James Nagy is a Professor of Mathematics and Computer Science at Emory University. He received his Ph.D. in Applied Mathematics from North Carolina State University in 1991. Before joining Emory University in 1999 he had postdoctoral research fellowships with the IMA at the University of Minnesota, with the NSF at the University of Maryland, and was on the faculty at Southern Methodist University. He is on the editorial boards of SIAM Journal on Scientific Computing (SISC), SIAM Journal on Matrix Analysis and Applications (SIMAX), and the Electronic Journal of Linear Algebra (ELA). His research interests include numerical linear algebra, structured matrix computations, and numerical solution of inverse problems in image processing. In addition to his many journal publications, he is co-author with Per Christian Hansen and Dianne O'Leary of the book "Image Deblurring: Matrices, Spectra and Filtering", published by SIAM.