Friday, October 31

MS12
Linear Algebra for Ill-Posed Problems and Image Processing

10:00 AM-12:00 PM
Room: Ballroom 2

Many problems in science and engineering are concerned with the determination of the internal structure of a system from exterior measurements. These problems typically are ill-posed. Their discretization can give rise to large severely ill-conditioned linear or nonlinear systems of equations. The computation of a meaningful approximate solution in the presence of errors in the data requires regularization. Recently, the development of special iterative methods for determining a regularized approximate solution of large-scale discrete ill-posed problems has received considerable attention, in particular for image processing applications. The purpose of this minisymposium to present an overview of state-of-the-art methods for the numerical solution of ill-posed problems with particular emphasis on the linear algebra involved.

Organizer: Daniela Calvetti,
Stevens Institute of Technology;
and Lothar Reichel,
Kent State University

10:00 Efficient Algorithms for Least-squares Type Problems

Gene H. Golub, Stanford University

10:30 A Regularizing Lanczos Iteration for Underdetermined Linear Systems

Daniela Calvetti and Lothar Reichel, Organizers; and F. Sgallari and G. Spaletta, Universita di Bologna, Italy

11:00 Numerical Linear Algebra and Constrained Deconvolution

Curtis R. Vogel, Montana State University; and James G. Nagy, Southern Methodist University

11:30 A Modular Solver for Constrained Regularization Problems in Image Restoration

Tony F. Chan and Peter Blomgren, University of California, Los Angeles