Related papers: Flexible Krylov Methods for Group Sparsity Regular…
In this paper we develop flexible Krylov methods for efficiently computing regularized solutions to large-scale linear inverse problems with an $\ell_2$ fit-to-data term and an $\ell_p$ penalization term, for $p\geq 1$. First we approximate…
This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…
Flexible Krylov methods are a common standpoint for inverse problems. In particular, they are used to address the challenges associated with explicit variational regularization when it goes beyond the two-norm, for example involving an…
The computation of sparse solutions of large-scale linear discrete ill-posed problems remains a computationally demanding task. A powerful framework in this context is the use of iteratively reweighted schemes, which are based on…
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…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e.,…
This paper presents two new augmented flexible (AF)-Krylov subspace methods, AF-GMRES and AF-LSQR, to compute solutions of large-scale linear discrete ill-posed problems that can be modeled as the sum of two independent random variables,…
For the linear inverse problem with sparsity constraints, the $l_0$ regularized problem is NP-hard, and existing approaches either utilize greedy algorithms to find almost-optimal solutions or to approximate the $l_0$ regularization with…
This paper is concerned with the regularization of large-scale discrete inverse problems by means of inexact Krylov methods. Specifically, we derive two new inexact Krylov methods that can be efficiently applied to unregularized or…
We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
High-quality reconstructions of signals and images with sharp edges are needed in a wide range of applications. To overcome the large dimensionality of the parameter space and the complexity of the regularization functional,…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…
Penalty functions or regularization terms that promote structured solutions to optimization problems are of great interest in many fields. Proposed in this work is a nonconvex structured sparsity penalty that promotes one-sparsity within…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…