This paper surveys an important class of methods that combine iterative projection methods
and variational regularization methods for large-scale inverse problems. Iterative methods …

In the framework of large-scale linear discrete ill-posed problems, Krylov projection methods
represent an essential tool since their development, which dates back to the early 1950's. In …

This paper presents a new efficient approach for the solution of the \ell_p-\ell_q minimization
problem based on the application of successive orthogonal projections onto generalized …

This paper introduces two new algorithms, belonging to the class of Arnoldi--Tikhonov
regularization methods, which are particularly appropriate for sparse reconstruction. The …

We consider the solution of linear discrete ill-posed systems of equations with a certain
tensor product structure. Two aspects of this kind of problems are investigated: They are …

Tikhonov regularization for projected solutions of large-scale ill-posed problems is
considered. The Golub--Kahan iterative bidiagonalization is used to project the problem …

Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed
problems with error-contaminated data. A regularization operator and a suitable value of a …

We develop a generalized hybrid iterative approach for computing solutions to large-scale
Bayesian inverse problems. We consider a hybrid algorithm based on the generalized …

This paper presents a new approach to computing an approximate solution of Tikhonov-
regularized large-scale ill-posed least-squares problems with a general regularization …

Image reconstruction problems, like image deblurring and computer tomography, are
usually ill-posed and require regularization. A popular approach to regularization is to …