Many problems that arise in image processing applications require
the solution of an ill-posed inverse problem, that is, one in which
minor noise or perturbations in the data may result in major
instabilities in the computed solution. Tikhonov regularization can
be used to stabilize the inverse solution. However, it is well known
that iterative schemes must be used to efficiently solve
large-scale, sparse, or structured problems. Furthermore, due to
physical properties of image processing, it is often desirable to
compute nonnegative solutions. We have developed a
constrained iterative Tikhonov scheme for image restoration (i.e.
deblurring) that incorporates nonnegativity, and we use
sophisticated state-of-the-art solvers for efficient implementation
and automatic selection of regularization parameters.