Image Deblurring with Krylov Subspace Methods
by Professor Per Christian Hansen,
Department of Informatics and Mathematical Modelling,
Technical University of Denmark

March 22nd (Thu.) 11:00 - 12:30am

Lecture room 1 (Room 1212), 12th floor, National Institute of Informatics, Japan

Image deblurring, i.e., reconstruction of a sharper image from a blurred and noisy one, involves the solution of a large and very ill-conditioned system of linear equations, and regularization is needed in order to compute a stable solution. Krylov subspace methods are often ideally suited for this task: their iterative nature is a natural way to handle such large-scale problems, and the underlying Krylov subspace provides a convenient mechanism to regularized the problem by projecting it onto a low-dimensional "signal subspace" adapted to the particular problem. In this talk we consider the three Krylov subspace methods CGLS, MINRES, and GMRES. We describe their regularizing properties, and we discuss some computational aspects such as preconditioning and stopping criteria.