Kristian Bredies // Veröffentlichungen

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Bisherige Veröffentlichungen

Bücher

Kristian Bredies und Dirk Lorenz

Mathematische Bildverarbeitung

Vieweg+Teubner, 445 Seiten, 2011. ISBN: 978-3-8348-1037-3

Kristian Bredies und Dirk Lorenz

Mathematical image processing

Birkhäuser, 473 Seiten, 2018. ISBN: 978-3-030-01457-5

Preprints

Kristian Bredies, José A. Iglesias und Daniel Walter. On extremal points for some vectorial total variation seminorms. Zur Veröffentlichung eingereicht, 2024.

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Kristian Bredies, Marcello Carioni, Martin Holler, Yury Korolev und Carola-Bibiane Schönlieb. A sparse optimization approach to infinite infimal convolution regularization. Zur Veröffentlichung eingereicht, 2023.

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Kristian Bredies und Hongpeng Sun. Accelerated Douglas-Rachford methods for the solution of convex-concave saddle-point problems. Zur Veröffentlichung eingereicht, 2016.

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Forschungsartikel

Kristian Bredies, Enis Chenchene und Emanuele Naldi. Graph and distributed extensions of the Douglas-Rachford method. Zur Veröffentlichung angenommen durch SIAM Journal on Optimization, 2024.

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Kristian Bredies, Jonathan Chirinos Rodriguez und Emanuele Naldi. On extreme points and representer theorems for the Lipschitz unit ball on finite metric spaces. Archiv der Mathematik, Online first, 2024.

Open Access

Kristian Bredies, Marcello Carioni, Silvio Fanzon und Daniel Walter. Asymptotic linear convergence of fully-corrective generalized conditional gradient methods. Mathematical Programming, 205(1-2):135-202, 2024.

Open Access

Kristian Bredies, José A. Iglesias und Gwenael Mercier. Boundedness and unboundedness in total variation regularization. Applied Mathematics and Optimization, 88(2):51, 2023.

Open Access

Kristian Bredies, Marcello Carioni, Silvio Fanzon und Francisco Romero. A generalized conditional gradient method for dynamic inverse problems with optimal transport regularization. Foundations of Computational Mathematics, 23(3):833-898, 2023.

Open Access

Kristian Bredies, Marcello Carioni und Silvio Fanzon. A superposition principle for the inhomogeneous continuity equation with Hellinger-Kantorovich-regular coefficients. Communications in Partial Differential Equations, 47(10):2023-2069, 2022.

Open Access

Kristian Bredies, Enis Chenchene, Dirk A. Lorenz und Emanuele Naldi. Degenerate preconditioned proximal point algorithms. SIAM Journal on Optimization, 32(3):2376-2401, 2022.

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Kristian Bredies, Marcello Carioni und Martin Holler. Regularization Graphs — A unified framework for variational regularization of inverse problems. Inverse Problems, 38(10):105006, 2022.

Open Access

Anna Pukaluk, Anna-Sophie Wittgenstein, Gerd Leitinger, Dagmar Kolb, Dominique Pernitsch, Sarah Schneider, Patrick Knöbelreiter, Verena Horak, Kristian Bredies, Gerhard Holzapfel, Thomas Pock und Gerhard Sommer. An ultrastructural 3D reconstruction method for observing the arrangement of collagen fibrils and proteoglycans in the human aortic wall under mechanical load. Acta Biomaterialia, 141:300-314, 2022.

Open Access

Carlos Milovic, Mathias Lambert, Christian Langkammer, Kristian Bredies, Pablo Irarrazaval und Cristian Tejos. Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM). Magnetic Resonance in Medicine, 87(1):457-473, 2021.

Open Access

Kristian Bredies, Marcello Carioni, Silvio Fanzon und Francisco Romero. On the extremal points of the ball of the Benamou-Brenier energy. Bulletin of the London Mathematical Society, 53(5):1436-1452, 2021.

Open Access

Robert Beinert und Kristian Bredies. Tensor-free proximal methods for lifted bilinear/quadratic inverse problems with applications to phase retrieval. Foundations of Computational Mathematics, 21(5):1181-1232, 2021.

Open Access

Kristian Bredies und Richard Huber. Convergence analysis of pixel-driven Radon and fanbeam transforms. SIAM Journal on Numerical Analysis, 59(3):1399-1432, 2021.

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Oliver Maier, Stefan M. Spann, Daniela Pinter, Thomas Gattringer, Nicole Hinteregger, Gerhard G. Thallinger, Christian Enzinger, Josef Pfeuffer, Kristian Bredies und Rudolf Stollberger. Non-linear fitting with joint spatial regularization in arterial spin labeling. Medical Image Analysis, 71:102067, 2021.

Open Access

Sandro Belz und Kristian Bredies. Approximation of the Mumford-Shah Functional by phase fields of bounded variation. Analysis and Applications, 19(2):183-217, 2021.

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Kristian Bredies und Martin Holler. Higher-order total variation approaches and generalisations. Inverse Problems, 36(12):123001, 2020.

Open Access

Kristian Bredies und Silvio Fanzon. An optimal transport approach for solving dynamic inverse problems in spaces of measures. ESAIM: Mathematical Modelling and Numerical Analysis, 54(6):2351-2382, 2020.

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Kristian Bredies, Robert Nuster und Raphael Watschinger. TGV-regularized inversion of the Radon transform for photoacoustic tomography. Biomedical Optics Express, 11(2):994-1019, 2020.

Open Access

Kristian Bredies und Marcello Carioni. Sparsity of solutions for variational inverse problems with finite-dimensional data. Calculus of Variations and Partial Differential Equations, 59:14, 2020.

Open Access

Kristian Bredies und David Vicente. A perfect reconstruction property for PDE-constrained total-variation minimization with application in Quantitative Susceptibility Mapping. ESAIM: Control, Optimisation and Calculus of Variations, 25:83, 2019.

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Stefan Spann, Xingfeng Shao, Danny Wang, Christoph Aigner, Matthias Schloegl, Kristian Bredies und Rudolf Stollberger. Robust single-shot acquisition of high resolution whole brain ASL images by combining time-dependent 2D CAPIRINHA sampling with spatio-temporal TGV reconstruction. NeuroImage, 116337, 2019.

Richard Huber, Georg Haberfehlner, Martin Holler, Gerald Kothleitner und Kristian Bredies. Total Generalized Variation regularization for multi-modal electron tomography. Nanoscale, 11:5617-5632, 2019.

Open Access

Oliver Maier, Jasper Schoormans, Matthias Schloegl, Gustav J. Strijkers, Andreas Lesch, Thomas Benkert, Tobias Block, Bram F. Coolen, Kristian Bredies und Rudolf Stollberger. Rapid $T_1$ quantification from high resolution 3D data with model‐based reconstruction. Magnetic Resonance in Medicine, 81(3):2072-2089, 2019.

Open Access

Andreas Lesch, Matthias Schloegl, Martin Holler, Kristian Bredies und Rudolf Stollberger. Ultrafast 3D Bloch-Siegert $B_1^+$ Mapping using Variational Modeling. Magnetic Resonance in Medicine, 81(2):881-892, 2019.

Open Access

Robert Beinert und Kristian Bredies. Non-convex regularization of bilinear and quadratic inverse problems by tensorial lifting. Inverse Problems, 35(1):015002, 2019.

Open Access

René Schranzer, Alexander Rauscher, Evelin Haimburger, Kristian Bredies, Gernot Reishofer und Günther Grabner. Noise reduction in FLAIR2 images using Total Generalized Variation, Gaussian and Wiener filtering. Zeitschrift für Medizinische Physik, 28(4):286-292, 2018.

Yiming Gao und Kristian Bredies. Infimal Convolution of Oscillation Total Generalized Variation for the Recovery of Images with Structured Texture. SIAM Journal on Imaging Sciences, 11(3):2021-2063, 2018.

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Kristian Bredies, Martin Holler, Martin Storath und Andreas Weinmann. Total Generalized Variation for Manifold-valued Data. SIAM Journal on Imaging Sciences, 11(3):1785-1848, 2018.

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C. Langkammer, F. Schweser, K. Shmueli, C. Kames, X. Li, L. Guo, C. Milovic, J. Kim, H. Wei, K. Bredies, S. Buch, Y. Guo, Z. Liu, J. Meineke, A. Rauscher, J. P. Marques und B. Bilgic. Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge. Magnetic Resonance in Medicine, 79(3):1661-1673, 2018.

G. Schramm, M. Holler, A. Rezaei, K. Vunckx, F. Knoll, K. Bredies, F. Boada und J. Nuyts. Evaluation of Parallel Level Sets and Bowsher's Method as Segmentation-Free Anatomical Priors for Time-of-Flight PET Reconstruction. IEEE Transactions on Medical Imaging, 37(2):590-603, 2018.

Stefan Spann, Kamil S. Kazimierski, Christoph S. Aigner, Markus Kraiger, Kristian Bredies und Rudolf Stollberger. Spatio-temporal TGV denoising for ASL perfusion imaging. NeuroImage, 157:81-96, 2017.

Matthias Schloegl, Martin Holler, Andreas Schwarzl, Kristian Bredies und Rudolf Stollberger. Infimal Convolution of Total Generalized Variation Functionals for dynamic MRI. Magnetic Resonance in Medicine, 78(1):142-155, 2017.

Betrachte bei Europe PMC

Kristian Bredies und Hongpeng Sun. A Proximal Point Analysis of the Preconditioned Alternating Direction Method of Multipliers. Journal of Optimization Theory and Applications, 173(3):878-907, 2017.

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Daniel Stäb, Steffen Bollmann, Christian Langkammer, Kristian Bredies und Markus Barth. Accelerated mapping of magnetic susceptibility using 3D planes-on-a-paddlewheel (POP) EPI at ultra-high field strength. NMR in Biomedicine, 30(4), 2017.

Ferdinand Schweser, Simon Daniel Robinson, Ludovic de Rochefort, Wei Lie und Kristian Bredies. An illustrated comparison of processing methods for phase MRI and QSM: removal of background field contributions from sources outside the region of interest. NMR in Biomedicine, 30(4), 2017.

Simon Daniel Robinson, Kristian Bredies, Diana Khabipova, Barbara Dymerska, José P. Marques und Ferdinand Schweser. An illustrated comparison of processing methods for MR phase imaging and QSM: combining array coil signals and phase unwrapping. NMR in Biomedicine, 30(4), 2017.

Open Access

Florian Knoll, Martin Holler, Thomas Koesters, Ricardo Otazo, Kristian Bredies und Daniel Sodickson. Joint MR-PET reconstruction using a multi-channel image regularizer. IEEE Transactions on Medical Imaging, 36(1):1-16, 2017.

Kristian Bredies, Barbara Kaltenbacher und Elena Resmerita. The least error method for sparse solution reconstruction. Inverse Problems, 32:094001, 2016.

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A. Crozier, C. M. Augustin, A. Neic, A. J. Prassl, M. Holler, T. E. Fastl, A. Hennemuth, K. Bredies, T. Kuehne, M. J. Bishop, S. A. Niederer und G. Plank. Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling. Annals of Biomedical Engineering, 44(1):58-70, 2016.

Open Access

Kristian Bredies und Martin Holler. A TGV-based framework for variational image decompression, zooming and reconstruction. Part I: Analytics. SIAM Journal on Imaging Sciences, 8(4):2814-2850, 2015.

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Kristian Bredies und Martin Holler. A TGV-based framework for variational image decompression, zooming and reconstruction. Part II: Numerics. SIAM Journal on Imaging Sciences, 8(4):2851-2886, 2015.

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Kristian Bredies, Dirk A. Lorenz und Stefan Reiterer. Minimization of non-smooth, non-convex functionals by iterative thresholding. Journal of Optimization Theory and Applications, 165(1):78-112, 2015.

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Christian Langkammer, Kristian Bredies, Benedikt A. Poser, Markus Barth, Gernot Reishofer, Audrey Peiwen Fan, Berkin Bilgic, Franz Fazekas, Caterina Mainero und Stefan Ropele. Fast Quantitative Susceptibility Mapping using 3D EPI and Total Generalized Variation. NeuroImage, 111:622-630, 2015.

Konstantinos Papafitsoros und Kristian Bredies. A study of the one dimensional total generalised variation regularisation problem. Inverse Problems and Imaging, 9(2):511-550, 2015.

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Kristian Bredies und Hongpeng Sun. Preconditioned Douglas-Rachford algorithms for TV and TGV regularized variational imaging problems. Journal of Mathematical Imaging and Vision, 52(3):317-344, 2015.

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Kristian Bredies und Hongpeng Sun. Preconditioned Douglas-Rachford splitting methods for convex-concave saddle-point problems. SIAM Journal on Numerical Analysis, 53(1):421-444, 2015.

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Kristian Bredies, Thomas Pock und Benedikt Wirth. A convex, lower semi-continuous approximation of Euler's Elastica energy. SIAM Journal on Mathematical Analysis, 47(1):566-613, 2015.

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Kristian Bredies. Recovering piecewise smooth multichannel images by minimization of convex functionals with total generalized variation penalty. Lecture Notes in Computer Science, 8293:44-77, 2014.

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Kristian Bredies und Martin Holler. Regularization of linear inverse problems with total generalized variation. Journal of Inverse and Ill-posed Problems, 22(6):871-913, 2014.

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Kristian Bredies, Marcus Wagner, Christian Schubert und Peter Ahnelt. Computer-assisted counting of retinal cells by automatic segmentation after TV denoising. BMC Ophthalmology, 13:59, 2013.

Open Access

Kristian Bredies. Symmetric tensor fields of bounded deformation. Annali di Matematica Pura ed Applicata, 192(5):815-851, 2013.

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Kristian Bredies, Thomas Pock und Benedikt Wirth. Convex relaxation of a class of vertex penalizing functionals. Journal of Mathematical Imaging and Vision, 47(3):278-302, 2013.

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Florian Knoll, Gerrit Schultz, Kristian Bredies, Daniel Gallichan, Maxim Zaitsev, Jürgen Hennig und Rudolf Stollberger. Reconstruction of undersampled radial PatLoc imaging using Total Generalized Variation. Magnetic Resonance in Medicine, 70(1):40-52, 2013.

Betrachte bei Europe PMC

Tuomo Valkonen, Kristian Bredies und Florian Knoll. Total Generalized Variation in Diffusion Tensor Imaging. SIAM Journal on Imaging Sciences, 6(1):487-525, 2013.

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Manuel Freiberger, Florian Knoll, Kristian Bredies, Hermann Scharfetter und Rudolf Stollberger. The Agile Library for Biomedical Image Reconstruction Using GPU Acceleration. Computing in Science & Engineering, 15(1):34-44, 2013.

Kristian Bredies und Hanna Pikkarainen. Inverse problems in spaces of measures. ESAIM: Control, Optimisation and Calculus of Variations, 19(1):190-218, 2013.

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Kristian Bredies und Mariya Zhariy. A discrepancy-based parameter adaptation and stopping rule for minimization algorithms aiming at Tikhonov-type regularization. Inverse Problems, 29:025008, 2013.

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Kristian Bredies, Yiqiu Dong und Michael Hintermüller. Spatially dependent regularization parameter selection in total generalized variation models for image restoration. International Journal of Computer Mathematics, 90(1):109-123, 2013.

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Kristian Bredies, Karl Kunisch und Tuomo Valkonen. Properties of $L^1$ - $\mathrm{TGV}^2$ : The one-dimensional case. Journal of Mathematical Analysis and Applications, 398(1):438-454, 2013.

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Heimo Wolinski, Kristian Bredies und Sepp D. Kohlwein. Quantitative imaging of lipid metabolism in yeast: from 4D analysis to high content screens of mutant libraries. Methods in Cell Biology, 108:345-365, 2012.

Florian Knoll, Christian Clason, Kristian Bredies, Martin Uecker und Rudolf Stollberger. Parallel Imaging with Nonlinear Reconstruction using Variational Penalties. Magnetic Resonance in Medicine, 67(1):34-41, 2012.

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Kristian Bredies und Martin Holler. A Total-Variation-based JPEG decompression model. SIAM Journal on Imaging Sciences, 5(1):366-393, 2012.

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Kristian Bredies und Heimo Wolinski. An active-contour based algorithm for the automated segmentation of dense yeast populations on transmission microscopy images. Computing and Visualization in Science, 14(7):341-352, 2011.

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Florian Knoll, Kristian Bredies, Thomas Pock und Rudolf Stollberger. Second order total generalized variation (TGV) for MRI. Magnetic Resonance in Medicine, 65(2):480-491, 2011.

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Kristian Bredies, Karl Kunisch und Thomas Pock. Total generalized variation. SIAM Journal on Imaging Sciences, 3(3):492-526, 2010.

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Kristian Bredies und Dirk A. Lorenz. Regularization with non-convex separable constraints. Inverse Problems, 25:085011, 2009.

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Kristian Bredies. Weak solutions of linear degenerate parabolic equations and an application in image processing. Communications on Pure and Applied Analysis, 8(4):1203-1229, 2009.

Kristian Bredies, Dirk A. Lorenz und Peter Maass. A generalized conditional gradient method and its connection to an iterative shrinkage method. Computational Optimization and Applications, 42(2):173-193, 2009.

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Kristian Bredies. A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space. Inverse Problems, 25:015005, 2009.

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Kristian Bredies und Dirk A. Lorenz. Linear convergence of iterative soft-thresholding. Journal of Fourier Analysis and Applications, 14(5-6):813-837, 2008.

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Kristian Bredies und Dirk A. Lorenz. Iterated hard shrinkage for minimization problems with sparsity constraints. SIAM Journal on Scientific Computing, 30(2):657-683, 2008.

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Thomas Bonesky, Kristian Bredies, Dirk A. Lorenz und Peter Maass. A generalized conditional gradient method for non-linear operator equations with sparsity constraints. Inverse Problems, 23(5):2041-2058, 2007.

Kristian Bredies, Dirk A. Lorenz und Peter Maass. Mathematical concepts of multiscale smoothing. Applied Computational and Harmonic Analysis, 19(2):141-161, 2005.

Elsevier Open Archive

Tagungsbeiträge

Enis Chenchene, Alireza Hosseini und Kristian Bredies. A hybrid proximal generalized conditional gradient method and application to total variation parameter learning. In: 2023 European Control Conference (ECC), pp. 322-327, 2023.

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Verena Horak und Kristian Bredies. A Two-Stage Classifier for Collagen in Electron Tomography Images using a Convolutional Neural Network and TV Segmentation. In: Proceedings of the ARW & OAGM Workshop 2019, pp. 209-210, 2019.

Open Access

Florian Knoll, Martin Holler, Thomas Koesters, Kristian Bredies und Daniel K. Sodickson. Simultaneous PET-MRI reconstruction with vectorial second order total generalized variation. In: Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), pp. 1-4, 2016.

Richard Huber, Martin Holler und Kristian Bredies. Graph-Laplacian minimisation for surface smoothing in 3D finite element tetrahedral meshes. In: Proceedings of the 1st OAGM-ARW Joint Workshop - Vision Meets Robotics, pp. 53-60, 2016.

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Kristian Bredies und Martin Holler. Artifact-Free Variational MPEG Decompression. In: Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, 9087:216-228, 2015.

René Ranftl, Kristian Bredies und Thomas Pock. Non-local total generalized variation for optical flow estimation. In: Computer Vision - ECCV 2014. Lecture Notes in Computer Science, 8689:439-454, 2014.

Clemens Schiffer und Kristian Bredies. Sinogram constrained TV-minimization for metal artifact reduction in CT. In: Proceedings of The 38th Annual Workshop of the Austrian Association for Pattern Recognition (ÖAGM), 2014.

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Kristian Bredies, Florian Knoll und Christian Langkammer. TGV regularization for variational approaches to quantitative susceptibility mapping. In: Proceedings of the 2nd International Workshop on MRI Phase Contrast & Quantitative Susceptibility Mapping (QSM). Ithaca, New York (USA), pp. 45-48, 2013.

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Tuomo Valkonen, Kristian Bredies und Florian Knoll. TGV for diffusion tensors: A comparison of fidelity functions. In: Recent Progress in Regularization Theory, Minisymposium M5 of the 6th International Conference Inverse Problems: Modeling and Simulation. Journal of Inverse and Ill-Posed Problems, 21(3):355-377, 2013.

Kristian Bredies und Martin Holler. A TGV Regularized Wavelet Based Zooming Model. In: Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, 7893:149-160, 2013.

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Kristian Bredies und Martin Holler. Artifact-free decompression and zooming of JPEG compressed images with total generalized variation. In: Computer Vision, Imaging and Computer Graphics. Theory and Application. Communications in Computer and Information Science, 359:242-258, 2013.

Kristian Bredies, Martin Holler, Florian Knoll, Karl Kunisch, Michael Pienn, Rudolf Stollberger und Tuomo Valkonen. Total generalized variation and applications to inverse problems in medical imaging. Oberwolfach Report 51/2012: Computational Inverse Problems, 9(4):3119-3121, 2012.

Kristian Bredies und Martin Holler. Artifact-free JPEG decompression with total generalized variation. Proceedings of VISAPP 2012 - International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, pp. 12-21, 2012.

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Kristian Bredies und Tuomo Valkonen. Inverse problems with second-order total generalized variation constraints. Proceedings of SampTA 2011 - 9th International Conference on Sampling Theory and Applications, Singapore, 2011.

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Kristian Bredies. Variational Imaging with $\mathrm{TGV}^2$ -regularization. Oberwolfach Report 07/2011: Trends in Mathematical Imaging and Surface Processing, 8(1):310-316, 2011.

Kristian Bredies. An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space. Journal of Inverse and Ill-Posed Problems, Minisymposium - Recent progress in regularization theory, 4th International Conference: Inverse Problems: Modeling and Simulation, Fethiye 2008, 17(1):19-26, 2009.

Kristian Bredies, Theodore Alexandrov, Jens Decker, Dirk A. Lorenz, und Herbert Thiele. Sparse deconvolution for peak picking and ion charge estimation in mass spectrometry. Proceedings of the 15th European Conference on Mathematics for Industry, 2008.

Dirk Lorenz und Kristian Bredies. On the convergence speed of iterative methods for linear inverse problems with sparsity constraints. Journal of Physics: Conference Series 124:012031, 2008.

Dirk Lorenz und Kristian Bredies. Iterated hard-thresholding for linear inverse problems with sparsity constraints. Proceedings in Applied Mathematics and Mechanics, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, 7(1):2060061-2060062, 2008.

M. Kulesh, B. Berkels, K. Bredies, C. Garbe, J. F. Acher, M. S. Diallo, M. Droske, M. Holschneider, J. Hron, C. Kondermann, P. Maass, N. Olischläger, H.-O. Peitgen, T. Preusser, M. Rumpf, F. Scherbaum, S. Turek. Inverse Problems and Parameter Identification in Image Processing. Mathematical Methods in Time Series Analysis and Digital Image Processing, Springer Verlag, 111-152, 2007.

Peter Maass, Thomas Bonesky, Kristian Bredies und Dirk Lorenz. On the minimization of non-convex, non-differentiable functionals with an application to SPECT. Oberwolfach Report 34/2006: Mathematical Methods in Tomography, Oberwolfach Reports, 3(3):2076-2080, 2006.

Kristian Bredies, Dirk A. Lorenz und Peter Maass. An optimal control problem in image processing. Proceedings in Applied Mathematics and Mechanics, 6:859-860, 2006.

Kristian Bredies, Dirk A. Lorenz und Peter Maass. An optimal control problem in medical image processing. Systems, Control, Modeling and Optimization Proceedings of the 22nd IFIP TC7 Conference held from July 18-22, 2005, in Turin, Italy, 2005.

Kristian Bredies, Dirk A. Lorenz, Peter Maass und Gerd Teschke. A partial differential equation for continuous non-linear shrinkage filtering and its application for analyzing MMG data. Proceedings of SPIE Conference Photonics East 2003, 5266:84-93, 2004.

Unveröffentlicht

Kristian Bredies und Martin Holler. A pointwise characterization of the subdifferential of the total variation functional, 2012.

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Kristian Bredies. A variational weak weighted derivative: Sobolev spaces and degenerate elliptic equations, 2008.

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