Kristian Bredies
University of Graz
AlgorithmImage (mathematics)PhysicsMathematical optimizationMathematical analysisInverse problemIterative reconstructionArtificial intelligenceNoise reductionPattern recognitionApplied mathematicsTotal generalized variationComputer visionMathematicsComputer scienceImage qualityHilbert spaceConvergence (routing)Regularization (mathematics)Image processing
133Publications
31H-index
4,111Citations
Publications 113
Newest
#1Carlos MilovicH-Index: 7
#2Mathias Lambert (UC: Pontifical Catholic University of Chile)
Last. Cristian Tejos (UC: Pontifical Catholic University of Chile)H-Index: 18
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PURPOSE The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts. METHODS QSM functionals are solved with linear and nonlinear L1-norm da...
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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 that with the correc...
1 CitationsSource
#1Oliver Maier (Graz University of Technology)H-Index: 3
#2Stefan Manfred Spann (Graz University of Technology)H-Index: 3
Last. Rudolf Stollberger (Graz University of Technology)H-Index: 16
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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 can be challenging. Especially standard fitting using non-linear least squares often fails in regions with poor SNR, resulting in noisy estimates of the quantitative maps. State-of-the-art fitting techniques improve the SNR by incorporating prior knowledge in the estimation process which typically leads to spatial blu...
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#1Georg HaberfehlnerH-Index: 13
#2Richard Huber (University of Graz)H-Index: 2
Last. Gerald KothleitnerH-Index: 10
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We develop a dynamic generalized conditional gradient method (DGCG) for dynamic inverse problems with optimal transport regularization. We consider the framework introduced in (Bredies and Fanzon, ESAIM: M2AN, 54:2351-2382, 2020), where the objective functional is comprised of a fidelity term, penalizing the pointwise in time discrepancy between the observation and the unknown in time-varying Hilbert spaces, and a regularizer keeping track of the dynamics, given by the Benamou-Brenier energy con...
3 Citations
#1Kristian BrediesH-Index: 31
#2Silvio Fanzon (University of Graz)H-Index: 2
Last. Silvio FanzonH-Index: 3
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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 valued curve and are dynamic in the sense that (i) the measured data takes values in a time dependent family of Hilbert spaces, and (ii) the forward operators are time dependent and map, for each time, Radon measures into the corresponding data space. The variational regularization we propose is based on dynamic (un-)bal...
3 CitationsSource
#1Kristian BrediesH-Index: 31
#2Marcello CarioniH-Index: 5
Last. Silvio FanzonH-Index: 3
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We study measure-valued solutions of the inhomogeneous continuity equation \partial_t \rho_t + {\rm div}(v\rho_t) = g \rho_twhere the coefficients vand gare of low regularity. A new superposition principle is proven for positive measure solutions and coefficients for which the recently-introduced dynamic Hellinger-Kantorovich energy is finite. This principle gives a decomposition of the solution into curves t \mapsto h(t)\delta_{\gamma(t)}that satisfy the characteristic system $\dot ...
3 Citations
#1Kristian Bredies (University of Graz)H-Index: 31
#2Tuomo ValkonenH-Index: 14
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 "sparse" penalization of optimal balancing from the first up to the kth distributional derivative and leads to desirable results when applied to image denoising, i.e., L^2fitting with TGV penalty. The present paper studies TGV of second order in the context of solving ill-posed linear inverse problems. Existence and st...
26 Citations
#1Kristian Bredies (University of Graz)H-Index: 31
#2Martin Holler (University of Graz)H-Index: 15
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 generalisations of TV were soon proposed and studied with increasing interest, which led to a variety of different approaches being available today. We review several of these approaches, discussing aspects ranging from functional-analytic foundations to regularisation ...
5 CitationsSource
#1Kristian Bredies (University of Graz)H-Index: 31
#2Robert NusterH-Index: 20
Last. Raphael Watschinger (University of Graz)H-Index: 1
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We propose and study a reconstruction method for photoacoustic tomography (PAT) based on total generalized variation (TGV) regularization for the inversion of the slice-wise 2D-Radon transform in 3D. The latter problem occurs for recently-developed PAT imaging techniques with parallelized integrating ultrasound detection where projection data from various directions is sequentially acquired. As the imaging speed is presently limited to 20 seconds per 3D image, the reconstruction of temporally-re...
1 CitationsSource