We consider flexible Krylov methods for efficiently computing regularized solutions to large-scale linear inverse problems with a p-norm penalization term, for p>=1. To handle general (non-square) l_p-regularized least-squares problems, we introduce a flexible Golub-Kahan approach and exploit it within a Krylov-Tikhonov hybrid framework. The key benefits of our approach are that efficient projection methods replace inner-outer schemes and expensive regularization parameter selection techniques can be avoided. Theoretical insights and numerical results from image deblurring are provided.

This presentation is part of Minisymposium “MS8 - Krylov Methods in Imaging: Inverse Problems, Data Assimilation, and Uncertainty Quantification (2 parts)”
organized by: Arvind Saibaba (North Carolina State University) , Julianne Chung (Virginia Tech) , Eric de Sturler (Virginia Tech) .

Authors:

Julianne Chung (Virginia Tech)

Silvia Gazzola (University of Bath)

Keywords:

computed tomography, image deblurring, image reconstruction, inverse problems, numerical linear algebra, statistical inverse estimation methods