27 citations · 91 across the 11 of their papers we have counts for
14 papers
Applications of multiscale hierarchical decomposition to blind deconvolution
Tobias Wolf, Stefan Kindermann, Elena Resmerita +1
The blind image deconvolution is a challenging, highly ill-posed nonlinear inverse problem. We introduce a Multiscale Hierarchical Decomposition Method (MHDM) that is iteratively s…
Nested Bregman Iterations for Decomposition Problems
Tobias Wolf, Derek Driggs, Kostas Papafitsoros +2
We consider the task of image reconstruction while simultaneously decomposing the reconstructed image into components with different features. A commonly used tool for this is a va…
Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise
Joel Barnett, Wen Li, Elena Resmerita +1
Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image proc…
Multiscale hierarchical decomposition methods for ill-posed problems
Stefan Kindermann, Elena Resmerita, Tobias Wolf
The Multiscale Hierarchical Decomposition Method (MHDM) was introduced as an iterative method for total variation regularization, with the aim of recovering details at various scal…
Nonconvex flexible sparsity regularization: theory and monotone numerical schemes
Daria Ghilli, Dirk A. Lorenz, Elena Resmerita
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general no…
On Hamilton-Jacobi PDEs and image denoising models with certain non-additive noise
Jérôme Darbon, Tingwei Meng, Elena Resmerita
We consider image denoising problems formulated as variational problems. It is known that Hamilton-Jacobi PDEs govern the solution of such optimization problems when the noise mode…
An entropic Landweber method for linear ill-posed problems
Martin Burger, Elena Resmerita, Martin Benning
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for…
Regularization of ill-posed problems with non-negative solutions
Christian Clason, Barbara Kaltenbacher, Elena Resmerita
This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of met…
Flexible sparse regularization
Dirk A. Lorenz, Elena Resmerita
The seminal paper of Daubechies, Defrise, DeMol made clear that spaces with and -powers of the corresponding norms are appropriate settings for dealing wit…
Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems
Barbara Kaltenbacher, Franz Rendl, Elena Resmerita
In this paper we present a method for the regularized solution of nonlinear inverse problems, based on Ivanov regularization (also called method of quasi solutions or constrained l…
Regularization by Discretization in Banach Spaces
Uno Hämarik, Barbara Kaltenbacher, Urve Kangro +1
We consider ill-posed linear operator equations with operators acting between Banach spaces. For solution approximation, the methods of choice here are projection methods onto fini…
Lavrentiev's regularization method in Hilbert spaces revisited
Bernd Hofmann, Barbara Kaltenbacher, Elena Resmerita
In this paper, we deal with nonlinear ill-posed problems involving monotone operators and consider Lavrentiev's regularization method. This approach, in contrast to Tikhonov's regu…
Morozov's principle for the augmented Lagrangian method applied to linear inverse problems
Klaus Frick, Dirk A. Lorenz, Elena Resmerita
The Augmented Lagrangian Method as an approach for regularizing inverse problems received much attention recently, e.g. under the name Bregman iteration in imaging. This work shows…
Discretization of variational regularization in Banach spaces
C. Poeschl, E. Resmerita, O. Scherzer
Consider a nonlinear ill-posed operator equation where is defined on a Banach space . In general, for solving this equation numerically, a finite dimensional approx…