Kristian Bredies // Publications
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Publications

Books

Mathematical image processing
Kristian Bredies and Dirk Lorenz

Mathematische Bildverarbeitung
Mathematical image processing

Textbook (in German)

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

Research articles

Yiming Gao and Kristian Bredies. Infimal convolution of oscillation total generalized variation for the recovery of images with structured texture. Submitted for publication, 2017.   [PDF logo] Download PDF
Kristian Bredies, Martin Holler, Martin Storath and Andreas Weinmann. Total Generalized Variation for Manifold-valued Data. Submitted for publication, 2017.   [PDF logo] Download PDF
Kristian Bredies and David Vicente. A perfect reconstruction property for PDE-constrained total-variation minimization with application in Quantitative Susceptibility Mapping. Submitted for publication, 2017.   [PDF logo] Download PDF
Kristian Bredies and Hongpeng Sun. Accelerated Douglas-Rachford methods for the solution of convex-concave saddle-point problems. Submitted for publication, 2016.   [PDF logo] Download PDF
G. Schramm, M. Holler, A. Rezaei, K. Vunckx, F. Knoll, K. Bredies, F. Boada and 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, Early Access, 2017.
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 and B. Bilgic. Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge. Magnetic Resonance in Medicine, Early View, 2017.
Stefan Spann, Kamil S. Kazimierski, Christoph S. Aigner, Markus Kraiger, Kristian Bredies and Rudolf Stollberger. Spatio-temporal TGV denoising for ASL perfusion imaging. NeuroImage, 157:81-96, 2017.
Matthias Schloegl, Martin Holler, Andreas Schwarzl, Kristian Bredies and Rudolf Stollberger. Infimal Convolution of Total Generalized Variation Functionals for dynamic MRI. Magnetic Resonance in Medicine, 78(1):142-155, 2017.   [EPMC logo] View at Europe PMC
Kristian Bredies and 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.   [PDF logo] Download PDF
Daniel Stäb, Steffen Bollmann, Christian Langkammer, Kristian Bredies and 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 and 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 and 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 logo] Open Access
Florian Knoll, Martin Holler, Thomas Koesters, Ricardo Otazo, Kristian Bredies and 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 and Elena Resmerita. The least error method for sparse solution reconstruction. Inverse Problems, 32:094001, 2016.   [PDF logo] Download PDF
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 and G. Plank. Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling. Annals of Biomedical Engineering, 44(1):58-70, 2016.   [Open Access logo] Open Access
Kristian Bredies and 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.   [PDF logo] Download PDF
Kristian Bredies and 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.   [PDF logo] Download PDF
Kristian Bredies, Dirk A. Lorenz and Stefan Reiterer. Minimization of non-smooth, non-convex functionals by iterative thresholding. Journal of Optimization Theory and Applications, 165(1):78-112, 2015.   [PDF logo] Download PDF
Christian Langkammer, Kristian Bredies, Benedikt A. Poser, Markus Barth, Gernot Reishofer, Audrey Peiwen Fan, Berkin Bilgic, Franz Fazekas, Caterina Mainero and Stefan Ropele. Fast Quantitative Susceptibility Mapping using 3D EPI and Total Generalized Variation. NeuroImage, 111:622-630, 2015.
Konstantinos Papafitsoros and Kristian Bredies. A study of the one dimensional total generalised variation regularisation problem. Inverse Problems and Imaging, 9(2):511-550, 2015.   [PDF logo] Download PDF
Kristian Bredies and 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.   [PDF logo] Download PDF
Kristian Bredies and Hongpeng Sun. Preconditioned Douglas-Rachford splitting methods for convex-concave saddle-point problems. SIAM Journal on Numerical Analysis, 53(1):421-444, 2015.   [PDF logo] Download PDF
Kristian Bredies, Thomas Pock and Benedikt Wirth. A convex, lower semi-continuous approximation of Euler's Elastica energy. SIAM Journal on Mathematical Analysis, 47(1):566-613, 2015.   [PDF logo] Download PDF
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.   [PDF logo] Download PDF
Kristian Bredies and Martin Holler. Regularization of linear inverse problems with total generalized variation. Journal of Inverse and Ill-posed Problems, 22(6):871-913, 2014.   [PDF logo] Download PDF
Kristian Bredies, Marcus Wagner, Christian Schubert and Peter Ahnelt. Computer-assisted counting of retinal cells by automatic segmentation after TV denoising. BMC Ophthalmology, 13:59, 2013.   [Open Access logo] Open Access
Kristian Bredies. Symmetric tensor fields of bounded deformation. Annali di Matematica Pura ed Applicata, 192(5):815-851, 2013.   [PDF logo] Download PDF
Kristian Bredies, Thomas Pock and Benedikt Wirth. Convex relaxation of a class of vertex penalizing functionals. Journal of Mathematical Imaging and Vision, 47(3):278-302, 2013.   [PDF logo] Download PDF
Florian Knoll, Gerrit Schultz, Kristian Bredies, Daniel Gallichan, Maxim Zaitsev, Jürgen Hennig and Rudolf Stollberger. Reconstruction of undersampled radial PatLoc imaging using Total Generalized Variation. Magnetic Resonance in Medicine, 70(1):40-52, 2013.   [EPMC logo] View at Europe PMC
Tuomo Valkonen, Kristian Bredies and Florian Knoll. Total Generalized Variation in Diffusion Tensor Imaging. SIAM Journal on Imaging Sciences, 6(1):487-525, 2013.   [PDF logo] Download PDF
Manuel Freiberger, Florian Knoll, Kristian Bredies, Hermann Scharfetter and Rudolf Stollberger. The Agile Library for Biomedical Image Reconstruction Using GPU Acceleration. Computing in Science & Engineering, 15(1):34-44, 2013.
Kristian Bredies and Hanna Pikkarainen. Inverse problems in spaces of measures. ESAIM: Control, Optimisation and Calculus of Variations, 19(1):190-218, 2013.   [PDF logo] Download PDF
Kristian Bredies and Mariya Zhariy. A discrepancy-based parameter adaptation and stopping rule for minimization algorithms aiming at Tikhonov-type regularization. Inverse Problems, 29:025008, 2013.   [PDF logo] Download PDF
Kristian Bredies, Yiqiu Dong and 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.   [PDF logo] Download PDF
Kristian Bredies, Karl Kunisch and Tuomo Valkonen. Properties of $L^1$ - $\mathrm{TGV}^2$ : The one-dimensional case. Journal of Mathematical Analysis and Applications, 398(1):438-454, 2013.   [PDF logo] Download PDF
Heimo Wolinski, Kristian Bredies and 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 and Rudolf Stollberger. Parallel Imaging with Nonlinear Reconstruction using Variational Penalties. Magnetic Resonance in Medicine, 67(1):34-41, 2012.   [PDF logo] Download PDF
Kristian Bredies and Martin Holler. A Total-Variation-based JPEG decompression model. SIAM Journal on Imaging Sciences, 5(1):366-393, 2012.   [PDF logo] Download PDF
Kristian Bredies and 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.   [PDF logo] Download PDF
Florian Knoll, Kristian Bredies, Thomas Pock and Rudolf Stollberger. Second order total generalized variation (TGV) for MRI. Magnetic Resonance in Medicine, 65(2):480-491, 2011.   [PDF logo] Download PDF
Kristian Bredies, Karl Kunisch and Thomas Pock. Total generalized variation. SIAM Journal on Imaging Sciences, 3(3):492-526, 2010.   [PDF logo] Download PDF
Kristian Bredies and Dirk A. Lorenz. Regularization with non-convex separable constraints. Inverse Problems, 25:085011, 2009.   [PDF logo] Download PDF
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 and Peter Maass. A generalized conditional gradient method and its connection to an iterative shrinkage method. Computational Optimization and Applications, 42(2):173-193, 2009.   [PDF logo] Download PDF
Kristian Bredies. A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space. Inverse Problems, 25:015005, 2009.   [PDF logo] Download PDF
Kristian Bredies and Dirk A. Lorenz. Linear convergence of iterative soft-thresholding. Journal of Fourier Analysis and Applications, 14(5-6):813-837, 2008.   [PDF logo] Download PDF
Kristian Bredies and Dirk A. Lorenz. Iterated hard shrinkage for minimization problems with sparsity constraints. SIAM Journal on Scientific Computing, 30(2):657-683, 2008.   [PDF logo] Download PDF
Thomas Bonesky, Kristian Bredies, Dirk A. Lorenz and 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 and Peter Maass. Mathematical concepts of multiscale smoothing. Applied Computational and Harmonic Analysis, 19(2):141-161, 2005.   [PDF logo] Download PDF

Conference proceedings

Florian Knoll, Martin Holler, Thomas Koesters, Kristian Bredies and 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 and 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.   [PDF logo] Download PDF
Kristian Bredies and 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 and 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.   [PDF logo] Download PDF
Clemens Schiffer and 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), 2016.   [PDF logo] Download PDF
Kristian Bredies, Florian Knoll and 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.   [PDF logo] Download PDF
Tuomo Valkonen, Kristian Bredies and 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 and 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.   [PDF logo] Download PDF
Kristian Bredies and 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 and 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 and 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.   [PDF logo] Download PDF
Kristian Bredies and 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.   [PDF logo] Download PDF
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, and 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 and 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 and 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 and 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 and Peter Maass. An optimal control problem in image processing. Proceedings in Applied Mathematics and Mechanics, 6:859-860, 2006.
Kristian Bredies, Dirk A. Lorenz and 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 and 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.

Unpublished

Kristian Bredies and Martin Holler. A pointwise characterization of the subdifferential of the total variation functional, 2012.   [PDF logo] Download PDF
Kristian Bredies. A variational weak weighted derivative: Sobolev spaces and degenerate elliptic equations, 2008.   [PDF logo] Download PDF