Related papers: Stopping criterion for iterative regularization of…
Accurate determination of the regularization parameter in inverse problems still represents an analytical challenge, owing mainly to the considerable difficulty to separate the unknown noise from the signal. We present a new approach for…
The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
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…
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…
This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
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…
In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…
In this work, in the context of Linear and Quadratic Programming, we interpret Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method. The resulting Proximal Stabilized IPM (PS-IPM) is…
This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…
We present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method, for solving ill-posed linear inverse problems. The method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive…
The bilinear form of a matrix function, namely $\mathbf{u}^\top f(A) \mathbf{v}$, appears in many scientific computing problems, where $\mathbf{u}, \mathbf{v} \in \mathbb{R}^n$, $A \in \mathbb{R}^{n \times n}$, and $f(z)$ is a given…
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…
In this paper we investigate stopping criteria for iterative decoding from a mutual information perspective. We introduce new iteration stopping rules based on an approximation of the mutual information between encoded bits and decoder soft…
The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decomposition to reduce computational complexity by projecting the…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
We consider stopping criteria that balance algebraic and discretization errors for the conjugate gradient algorithm applied to high-order finite element discretizations of Poisson problems. Firstly, we introduce a new stopping criterion…
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\| \…