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.
