Related papers: Inverse problems with second-order Total Generaliz…
In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously…
We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters…
For linear inverse problem with Gaussian random noise we show that Tikhonov regularization algorithm is minimax in the class of linear estimators and is asymptotically minimax in the sense of sharp asymptotic in the class of all estimators.…
In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…
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…
Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The…
In this paper we present a globally convergent algorithm for the computation of a minimizer of the Tikhonov functional with sparsity promoting penalty term for nonlinear forward operators in Banach space. The dual TIGRA method uses a…
The Tikhonov regularization of linear ill-posed problems with an $\ell^1$ penalty is considered. We recall results for linear convergence rates and results on exact recovery of the support. Moreover, we derive conditions for exact support…
We explore the use of the recently proposed "total nuclear variation" (TNV) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued…
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…
Travel-time tomography forces a trade-off between mesh resolution and stability in which the regularizer choice dominates what can be recovered. We introduce MIMIR, a differentiable framework that represents the 2D velocity field as a…
In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its Total Symmetric…
In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations $\gdag = F(\udag)$ where $\gdag$ is an integrable, non-negative function. We assume that data are drawn from a Poisson process with density $t\gdag$…
This paper deals with a second order dynamical system with a Tikhonov regularization term in connection to the minimization problem of a convex Fr\'echet differentiable function. The fact that beside the asymptotically vanishing damping we…
It is well-known in practice, that L^1 data fitting leads to improved robustness compared to standard L^2 data fitting. However, it is unclear whether resulting algorithms will perform as well in case of regular data without outliers. In…
This paper is concerned with solving ill-posed tensor linear equations. These kinds of equations may appear from finite difference discretization of high-dimensional convection-diffusion problems or when partial differential equations in…
The conjugate gradient (CG) method is commonly used for the rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very…