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Reconstructing high-quality images with sharp edges requires the use of edge-preserving constraints in the regularized form of the inverse problem. The use of the $\ell_q$-norm on the gradient of the image is a common such constraint. For…
When reconstructing images from noisy measurements, such as in medical scans or scientific imaging, we face an inverse problem: recovering an unknown image from indirect, corrupted observations. These problems are typically ill-posed,…
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the…
For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations…
Model-based reconstruction plays a key role in compressed sensing (CS) MRI, as it incorporates effective image regularizers to improve the quality of reconstruction. The Plug-and-Play and Regularization-by-Denoising frameworks leverage…
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…
Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
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 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,…
Subspace recycling iterative methods and other subspace augmentation schemes are a successful extension to Krylov subspace methods in which a Krylov subspace is augmented with a fixed subspace spanned by vectors deemed to be helpful in…
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,…
Augmented Krylov subspace methods aid in accelerating the convergence of a standard Krylov subspace method by including additional vectors in the search space. A residual projection framework based on residual (Petrov-) Galerkin constraints…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…
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…
We present a new Krylov subspace recycling method for solving a linear system of equations, or a sequence of slowly changing linear systems. Our approach is to reduce the computational overhead of recycling techniques while still benefiting…
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…
Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include the computation of inner-products, which become costly when the number of…