Related papers: Generalized hybrid iterative methods for large-sca…
Solving large-scale Bayesian inverse problems presents significant challenges, particularly when the exact (discretized) forward operator is unavailable. These challenges often arise in image processing tasks due to unknown defects in the…
When solving ill-posed inverse problems, a good choice of the prior is critical for the computation of a reasonable solution. A common approach is to include a Gaussian prior, which is defined by a mean vector and a symmetric and positive…
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…
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…
We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems,…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
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…
The Golub-Kahan-Tikhonov method is a popular solution technique for large linear discrete ill-posed problems. This method first applies partial Golub-Kahan bidiagonalization to reduce the size of the given problem and then uses Tikhonov…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace…
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 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…
The hybrid LSMR algorithm is proposed for large-scale general-form regularization. It is based on a Krylov subspace projection method where the matrix $A$ is first projected onto a subspace, typically a Krylov subspace, which is implemented…
This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…
Iterative hybrid projection methods have proven to be very effective for solving large linear inverse problems due to their inherent regularizing properties as well as the added flexibility to select regularization parameters adaptively. In…
This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
We propose the generalized quadrature methods for numerical solution of singular integral equation of Abel type. We overcome the singularity using the analytical calculation of the singular integral expression. The problem of solution of…
This paper is concerned with solving ill-posed tensor linear equations. These kinds of equations may appear from finite difference discretization of high-dimensional convection-diffusion problems or when partial differential equations in…
We present a class of algorithms based on rational Krylov methods to compute the action of a generalized matrix function on a vector. These algorithms incorporate existing methods based on the Golub-Kahan bidiagonalization as a special…