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

James Nagy (Emory University) presents as part of the UBC Department of Computer Science's Distinguished Lecture Series, December 1, 2011.

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.