New flexible and inexact Golub-Kahan algorithms for inverse problems

This paper introduces a new class of algorithms for solving large-scale
linear inverse problems based on new flexible and inexact Golub-Kahan
factorizations. The proposed methods iteratively compute regularized solutions
by approximating a solution to (re)weighted least squares problems via
projection onto adaptively generated subspaces, where the constraint subspaces
for the residuals are (formally) equipped with iteration-dependent
preconditioners or inexactness. The new solvers offer a flexible and inexact
Krylov subspace alternative to other existing Krylov-based approaches for
handling general data fidelity functionals, e.g., those expressed in the
$p$-norm. Numerical experiments in imaging applications, such as image
deblurring and computed tomography, highlight the effectiveness and
competitiveness of the proposed methods with respect to other popular methods.