228 citations · 571 across the 28 of their papers we have counts for
29 papers
On extreme points and representer theorems for the Lipschitz unit ball on finite metric spaces
Kristian Bredies, Jonathan Chirinos Rodriguez, Emanuele Naldi
In this note, we provide a characterization for the set of extreme points of the Lipschitz unit ball in a specific vectorial setting. While the analysis of the case of real-valued…
A sparse optimization approach to infinite infimal convolution regularization
Kristian Bredies, Marcello Carioni, Martin Holler +2
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 regul…
A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems
Yakun Dong, Kristian Bredies, Hongpeng Sun
In this article, we propose and study a stochastic and relaxed preconditioned Douglas--Rachford splitting method to solve saddle-point problems that have separable dual variables.…
Graph and distributed extensions of the Douglas-Rachford method
Kristian Bredies, Enis Chenchene, Emanuele Naldi
In this paper, we propose several graph-based extensions of the Douglas-Rachford splitting (DRS) method to solve monotone inclusion problems involving the sum of maximal monoto…
A hybrid proximal generalized conditional gradient method and application to total variation parameter learning
Kristian Bredies, Enis Chenchene, Alireza Hosseini
In this paper we present a new method for solving optimization problems involving the sum of two proper, convex, lower semicontinuous functions, one of which has Lipschitz continuo…
A Second-Order TGV Discretization with Rotational Invariance Property
Alireza Hosseini, Kristian Bredies
In this work, we propose a new discretization for second-order total generalized variation (TGV) with some distinct properties compared to existing discrete formulations. The intro…
Boundedness and unboundedness in total variation regularization
Kristian Bredies, José A. Iglesias, Gwenael Mercier
We consider whether minimizers for total variation regularization of linear inverse problems belong to even if the measured data does not. We present a simple proof of b…
Regularization Graphs -- A unified framework for variational regularization of inverse problems
Kristian Bredies, Marcello Carioni, Martin Holler
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow t…
Asymptotic linear convergence of fully-corrective generalized conditional gradient methods
Kristian Bredies, Marcello Carioni, Silvio Fanzon +1
We propose a fully-corrective generalized conditional gradient method (FC-GCG) for the minimization of the sum of a smooth, convex loss function and a convex one-homogeneous regula…
Degenerate Preconditioned Proximal Point algorithms
Kristian Bredies, Enis Chenchene, Dirk A. Lorenz +1
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild…
A generalized conditional gradient method for dynamic inverse problems with optimal transport regularization
Kristian Bredies, Marcello Carioni, Silvio Fanzon +1
We develop a dynamic generalized conditional gradient method (DGCG) for dynamic inverse problems with optimal transport regularization. We consider the framework introduced in (Bre…
Non-linear fitting with joint spatial regularization in Arterial Spin Labeling
Oliver Maier, Stefan M Spann, Daniela Pinter +7
Multi-Delay single-shot arterial spin labeling (ASL) imaging provides accurate cerebral blood flow (CBF) and, in addition, arterial transit time (ATT) maps but the inherent low SNR…
A superposition principle for the inhomogeneous continuity equation with Hellinger-Kantorovich-regular coefficients
Kristian Bredies, Marcello Carioni, Silvio Fanzon
We study measure-valued solutions of the inhomogeneous continuity equation where the coefficients and are of low regularity. A ne…
Inverse problems with second-order Total Generalized Variation constraints
Kristian Bredies, Tuomo Valkonen
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "spars…
Convergence analysis of pixel-driven Radon and fanbeam transforms
Kristian Bredies, Richard Huber
This paper presents a novel mathematical framework for understanding pixel-driven approaches for the parallel beam Radon transform as well as for the fanbeam transform, showing tha…
Higher-order total variation approaches and generalisations
Kristian Bredies, Martin Holler
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. Whe…
Tensor-Free Proximal Methods for Lifted Bilinear/Quadratic Inverse Problems with Applications to Phase Retrieval
Robert Beinert, Kristian Bredies
We propose and study a class of novel algorithms that aim at solving bilinear and quadratic inverse problems. Using a convex relaxation based on tensorial lifting, and applying fir…
On the extremal points of the ball of the Benamou-Brenier energy
Kristian Bredies, Marcello Carioni, Silvio Fanzon +1
In this paper we characterize the extremal points of the unit ball of the Benamou--Brenier energy and of a coercive generalization of it, both subjected to the homogeneous continui…
Approximation of the Mumford-Shah Functional by Phase Fields of Bounded Variation
Sandro Belz, Kristian Bredies
In this paper we introduce a new phase field approximation of the Mumford-Shah functional similar to the well-known one from Ambrosio and Tortorelli. However, in our setting the ph…
An optimal transport approach for solving dynamic inverse problems in spaces of measures
Kristian Bredies, Silvio Fanzon
In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure va…
Sparsity of solutions for variational inverse problems with finite-dimensional data
Kristian Bredies, Marcello Carioni
In this paper we characterize sparse solutions for variational problems of the form , where is a locally convex space, is a…
Non-convex regularization of bilinear and quadratic inverse problems by tensorial lifting
Robert Beinert, Kristian Bredies
Considering the question: how non-linear may a non-linear operator be in order to extend the linear regularization theory, we introduce the class of dilinear mappings, which covers…
Infimal convolution of oscillation total generalized variation for the recovery of images with structured texture
Yiming Gao, Kristian Bredies
We propose a new type of regularization functional for images called oscillation total generalized variation (TGV) which can represent structured textures with oscillatory characte…
Total Generalized Variation for Manifold-valued Data
K. Bredies, M. Holler, M. Storath +1
In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data in a discrete setting. We provide an axiomatic appro…