Related papers: Sampled Tikhonov Regularization for Large Linear I…
This paper presents an error analysis of classical and learned Tikhonov regularization schemes for inverse problems. We first demonstrate, both theoretically and numerically, that using a fixed regularization parameter across varying noise…
Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for…
Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…
We study filter based regularization methods for linear ill-posed problems between Hilbert spaces. We derive optimal order conditions under a-priori choice rules for the regularization parameter. Such analysis is applied to the fractional…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…
The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively…
We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and…
Transformation Synchronization is the problem of recovering absolute transformations from a given set of pairwise relative motions. Despite its usefulness, the problem remains challenging due to the influences from noisy and outlier…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Coherent techniques for searches of gravitational-wave bursts effectively combine data from several detectors, taking into account differences in their responses. The efforts are now focused on the maximum likelihood principle as the most…
Primal-dual splitting involving proximity operators in order to be able to find some approximation to the minimizer for a general form of Tikhonov type functional is in the focus of this work. This approximation is produced by a pair of…
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…
This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of…