Related papers: Tikhonov regularization-based reconstruction of pa…
In this paper, we develop a framework for the discretization of a mixed formulation of quasi-reversibility solutions to ill-posed problems with respect to Poisson's equations. By carefully choosing test and trial spaces a formulation that…
Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…
This study outlines a numerical methodology aimed at rectifying the neutron scattering cross-sections of fundamental elements across a range of low neutron energies typically employed in general neutron scattering experiments. By using the…
Total variation(TV) regularization is applied to X-Ray computed tomography(CT) in an effort to reduce metal artifacts. Tikhonov regularization with $L^2$ data fidelity term and total variation regularization is augmented in this novel model…
The nucleon mass corrections are calculated to all polarized structure functions for neutral and charged current deep inelastic scattering in lowest order in the coupling constant. The impact of the target mass corrections on the general…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
Compton scatter tomography is an emerging technique with attractive applications in several fields in imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality in three dimensions with a…
Thermal neutron total scattering experiments of light and heavy water were reproduced using the CSNS in-house Monte Carlo thermal neutron transport code, Prompt, with a focus on the instrumental detector response and the accurate derivation…
Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers…
Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications. When first introduced as a regulariser, higher-order…
Radiative corrections to neutrino deep inelastic scattering are revisited. One-loop electroweak corrections are re-calculated within the automatic SANC system. Terms with mass singularities are treated including higher order leading…
We present DARTR: a Data Adaptive RKHS Tikhonov Regularization method for the linear inverse problem of nonparametric learning of function parameters in operators. A key ingredient is a system intrinsic data-adaptive (SIDA) RKHS, whose norm…
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an…
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…
It is common to have to process signals, whose values are points on the 3-D sphere. We consider a Tikhonov-type regularization model to smoothen or interpolate sphere-valued signals defined on arbitrary graphs. We propose a convex…
This paper addresses Tikhonov like regularization methods with convex penalty functionals for solving nonlinear ill-posed operator equations formulated in Banach or, more general, topological spaces. We present an approach for proving…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…