Regularization replaces the original ill-posed problem by the minimization problem with a fidelity and a regularization term. The use of a $p$-norm for the fidelity term, and a $q$-norm for the regularization term, has received considerable attention. The trade-off between these terms is determined by a parameter. In this talk we discuss how this parameter can be determined using the discrepancy principle. We conside $p=2$ and $0<q\leq 2$, observe that $0<q<1$ induces a non-convex problem.

This presentation is part of Minisymposium “MS34 - Numerical Linear Algebra techniques for Image Restoration and Reconstruction (2 parts)”
organized by: Caterina Fenu (University of Cagliari) , Marco Donatelli (University of Insubria) .

Authors:

Alessandro Buccini (Kent State University)

Lothar Reichel (Kent State University)

Keywords:

generalized krylov subspaces, image deblurring, image reconstruction, inverse problems, nonlinear optimization, numerical linear algebra