Related papers: Convergence rates for inverse Problems in Hilbert …
This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…
We study the behaviour of Tikhonov regularisation on topological spaces with multiple regularisation terms. The main result of the paper shows that multi-parameter regularisation is well-posed in the sense that the results depend…
In a Hilbert space, we provide a fast dynamic approach to the hierarchical minimization problem which consists in finding the minimum norm solution of a convex minimization problem. For this, we study the convergence properties of the…
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…
We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the iterates via minimization problems with uniformly convex penalty term. The penalty term is allowed to be non-smooth to include $L^1$ and total…
In a Hilbert framework, for convex differentiable optimization, we consider accelerated gradient methods obtained by combining temporal scaling and averaging techniques with Tikhonov regularization. We start from the continuous steepest…
In this article we propose a novel nonstationary iterated Tikhonov (NIT) type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear operators acting between Hilbert spaces. Geometrical…
We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing flow of option price information into the well-accepted local volatility model of Dupire. This leads to…
In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…
This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…
The theory of spectral filtering is a remarkable tool to understand the statistical properties of learning with kernels. For least squares, it allows to derive various regularization schemes that yield faster convergence rates of the excess…
Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successful and theoretically best-understood method is convex…
Recovering a function or high-dimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel…
Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…
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…
In a real Hilbert space setting, we investigate the asymptotic behavior of the solutions of the classical Arrow-Hurwicz differential system combined with Tikhonov regularizing terms. Under some newly proposed conditions on the Tikhonov…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.
In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…