Related papers: Tikhonov Regularization of Circle-Valued Signals
We study the choice of the regularisation parameter for linear ill-posed problems in the presence of data noise and operator perturbations, for which a bound on the operator error is known but the data noise-level is unknown. We introduce a…
In this article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
In this paper, in the setting of Hilbert spaces, we consider a Tikhonov regularized second-order plus first-order primal-dual dynamical system with asymptotically vanishing damping for a linear equality constrained convex optimization…
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with…
We consider a statistical inverse learning problem, where the task is to estimate a function $f$ based on noisy point evaluations of $Af$, where $A$ is a linear operator. The function $Af$ is evaluated at i.i.d. random design points $u_n$,…
This paper deals with a Tikhonov regularized second-order plus first-order primal-dual dynamical system with time scaling for separable convex optimization problems with linear equality constraints. This system consists of two second-order…
There has been tremendous research on the design of image regularizers over the years, from simple Tikhonov and Laplacian to sophisticated sparsity and CNN-based regularizers. Coupled with a model-based loss function, these are typically…
In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via…
By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bending energy is used as a stabilizing term in Tikhonov…
We study strategies for increasing the precision in the blurring models by maintaining a complexity in the related numerical linear algebra procedures (matrix-vector product, linear system solution, computation of eigenvalues etc.) of the…
In this paper the approximate solution of the heat exchange problem by A.N. Tikhonov regularization method is presented. The errror estimation of this approximate is obtained.
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of…
A novel theoretical framework, the inverse problem approach, is proposed to calculate non-perturbative quantities in quantum chromodynamics (QCD). Based on the dispersion relation of quantum field theory, this approach determines unknown…
We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…
The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and…
In this paper, based on the Tikhonov regularization technique, we study a monotone general variational inequality (GVI) by considering an associated strongly monotone GVI, depending on a regularization parameter $\alpha,$ such that the…
We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the…
We deal with a boundary detection problem arising in nondestructive testing of materials. The problem consists in recovering an unknown portion of the boundary, where a Robin condition is satisfied, with the use of a Cauchy data pair…