TU BRAUNSCHWEIG

Veröffentlichungen

Preprints

  1. A Sinkhorn-Newton method for entropic optimal transport
    Christoph Brauer, Christian Clason, Dirk A. Lorenz und Benedikt Wirth
    Eingereicht, Oktober 2017
    [arXiv.org/abs/1710.06635].
  2. A Primal-Dual Homotopy Algorithm for ℓ1-Minimization with ℓ-Constraints
    Christoph Brauer, Dirk A. Lorenz und Andreas M. Tillmann
    Eingereicht, Oktober 2016
    [arXiv.org/abs/1610.10022, OO].
  3. Linear convergence of the Randomized Sparse Kaczmarz method
    Frank Schöpfer und Dirk A. Lorenz
    Eingereicht, Oktober 2016
    [arXiv.org/abs/1610.02889].

Artikel in referierten Zeitschriften

  1. An extended Perona-Malik model based on probabilistic models
    Lars M. Mescheder und Dirk A. Lorenz
    Erscheint in Journal of Mathematical Imaging and Vision, 2017
    [arXiv.org/abs/1612.06176].
  2. Flexible sparse regularization
    Dirk A. Lorenz und Elena Resmerita
    Inverse Problems, 33(1), 2016
    [doi, arXiv.org/abs/1601.04429].
  3. How to be best in the OECD Better Life Index?
    Jan Lorenz, Christoph Brauer und Dirk A. Lorenz
    Social Indicators Research, 2016
    [doi, arXiv.org/abs/1608.04556]
  4. An inertial forward-backward method for monotone inclusions
    Dirk A. Lorenz und Thomas Pock
    Journal of Mathematical Imaging and Vision, 51(2):311-325, 2015
    [doi, arXiv.org/abs/1403.3522].
  5. Computing and analyzing recoverable supports for sparse reconstruction
    Christian Kruschel und Dirk A. Lorenz
    Advances in Computational Mathematics, 41(6):1119-1144, 2015
    [doi, arXiv.org/abs/1309.2460].
  6. Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized x-ray CT
    Jakob S. Jørgensen, Christian Kruschel und Dirk A. Lorenz
    Inverse Problems in Science and Engineering, 2014
    [doi, arXiv.org/abs/1409.0214].
  7. Data fusion of surface normals and point coordinates for deflectometric measurements
    Birgit Komander, Dirk A. Lorenz, Marc Fischer, Marcus Petz und Rainer Tutsch
    Journal of Sensors and Sensor Systems, 3:281-290, 2014
    [doi].
  8. Imaging with Kantorovich-Rubinstein discrepancy
    Jan Lellmann, Dirk A. Lorenz, Carola Schönlieb und Tuomo Valkonen
    SIAM Journal on Imaging Sciences, 7(4):2833-2859, 2014
    [doi,arXiv.org/abs/1407.0221].
  9. Minimization of non-smooth, non-convex functionals by iterative thresholding
    Kristian Bredies, Dirk A. Lorenz und Stefan Reiterer
    Journal of Optimization Theory and Applications, 165(1),78-112, 2015
    [doi, DFG SPP 1324 Preprint 10]
  10. The linearized Bregman method via split feasibility problems
    Dirk A. Lorenz, Frank Schöpfer und Stephan Wenger
    SIAM Journal in Imaging Sciences, 7(2) 2014
    [doi,arXiv.org/abs/1309.2094].
  11. Observer-independent quantification of insulin granule exocytosis and pre-exocytotic mobility by TIRF microscopy
    Magnus Matz, Kirstin Schumacher, Kathrin Hatlapatka, Dirk A. Lorenz, Knut Baumann, und Ingo Rustenbeck
    Microscopy and Microanalysis, 20(1):206–218, 2014
    [doi].
  12. Solving Basis Pursuit: Subgradient Algorithm, Heuristic Optimality Check, and Solver Comparison
    Dirk A. Lorenz, Marc E. Pfetsch und Andreas M. Tillmann
    ACM Transaction on Mathematical Software, 41(2), 2015
    [doi, OO Preprint].
  13. An Infeasible-Point Subgradient Method Using Adaptive Approximate Projections
    Dirk A. Lorenz, Marc E. Pfetsch und Andreas M. Tillmann
    Computational Optimization and Applications, 57(2):271-306, 2014
    [doi, arXiv.org/abs/1104.5351].
  14. Fast image-based modeling of astronomic nebulae
    Stephan Wenger, Dirk A. Lorenz und Marcus Magnor
    Computer Graphics Forum, 32(7), 2013.
  15. Necessary conditions for variational regularization schemes
    Dirk A. Lorenz und Nadja Worliczek
    Inverse Problems, 20:075016pp, 2013
    [doi, arXiv.org/abs/1204.0649].
  16. Constructing test instances for Basis Pursuit Denoising
    Dirk A. Lorenz
    IEEE Transactions on Signal Processing, 61(5):1210-1214, 2013
    [doi, arXiv.org/abs/1103.2897]
    Code zum Reproduzieren der Abbildungen ist hier (zip, 1 MByte).
  17. Visualization of astronomical nebulae via distributed multi-GPU compressed sensing tomography
    Stephan Wenger, Marco Ament, Stefan Guthe, Dirk A. Lorenz, Andreas Tillmann, Daniel Weiskopf und Marcus Magnor
    IEEE Transactions on Visualization and Computer Graphics, 18(12):2188–2197, 2012.
    [doi]
  18. Gradient descent methods based on quadratic approximations of Tikhonov functionals with sparsity constraints: theory and numerical comparison of stepsize rules
    Dirk A. Lorenz, Peter Maass und Pham Q. Muoi
    Electronic Transactions on Numerical Analysis, 39:437-463, 2012.
  19. Image Sequence Interpolation based on Optical Flow, Segmentation, and Optimal Control
    Kanglin Chen und Dirk A. Lorenz
    IEEE Transactions on Image Processing, 21(3):1020-1030, 2012.
    [doi]
  20. Morozov's principle for the augmented Lagrangian method applied to linear inverse problems
    Klaus Frick, Dirk A. Lorenz und Elena Resmerita
    SIAM Multiscale Modeling and Simulation, 9(4):1528-1548, 2011.
    [doi, arXiv.org/abs/1010.5181]
  21. Beyond convergence rates: Exact inversion with Tikhonov regularization with sparsity constraints
    Dirk A. Lorenz, Stefan Schiffler und Dennis Trede
    Inverse Problems, 27:085009, 2011
    [doi, arXiv.org/abs/1001.3276]
  22. Image sequence interpolation using optimal control
    Kanglin Chen und Dirk A. Lorenz
    Journal of Mathematical Imaging and Vision 41(3):222-238, 2011
    [doi, arXiv.org/abs/1008.0548]
  23. Heuristic parameter-choice rules for convex variational regularization based on error estimates
    Bangti Jin and Dirk A. Lorenz
    SIAM Journal on Numerical Analysis, 48(3):1208-1229, 2010
    [doi, arXiv.org/abs/1001.5346]
  24. Error estimates for joint Tikhonov- and Lavrentiev-regularization of constrained control problems
    Dirk A. Lorenz und Arnd Rösch
    Applicable Analysis, 89(11):1679-1692, 2010
    [arXiv.org/abs/0909.4648]
  25. A projection proximal-point algorithm for l^1-minimization
    Dirk A. Lorenz
    Numerical Functional Analysis and Optimization, 31(2):172-190, 2010
    [doi, arXiv.org/abs/0904.1523]
    m-File mit ppp_l1.m
  26. On Conditions for Convergence to Consensus
    Dirk A. Lorenz and Jan Lorenz
    IEEE Transactions on Automatic Control, 55(7):1651-1656, 2010
    [doi, arXiv.org/abs/0803.2211]
  27. Inline hologram reconstruction with sparsity constraints
    Loic Denis, Dirk A. Lorenz, Eric Thiebaut, Corinne Fournier und Dennis Trede.
    Optics Letters, 34(22):3475–3477,2009
    [doi]
  28. Elastic-Net Regularization: Error estimates and Active Set Methods
    Bangti Jin, Dirk A. Lorenz und Stefan Schiffler
    Inverse Problems, 25(11):115022 (26pp), 2009
    [doi, arXiv.org/abs/0905.0796]
  29. Greedy Solution of Ill-Posed Problems: Error Bounds and Exact Inversion
    Loic Denis, Dirk A. Lorenz und Dennis Trede
    Inverse Problems, 25(11):115017 (24pp), 2009
    [doi, arXiv.org/abs/0904.0154]
  30. Regularization with non-convex separable constraints
    Kristian Bredies und Dirk A. Lorenz
    Inverse Problems, 25(8):085011 (14pp), 2009
    [doi,SPP 1324 Preprint 11]
  31. Optimal convergence rates for Tikhonov regularization in Besov scales
    Dirk A. Lorenz und Dennis Trede
    Journal of Inverse and Ill Posed Problems, 17(1):69-76, 2009
    [doi]
  32. On the role of sparsity in inverse problems
    Dirk A. Lorenz
    Journal of Inverse and Ill-Posed Problems, 17(1):61-68, 2009
    [doi]
  33. A generalized conditional gradient method and its connection to an iterative shrinkage method
    Kristian Bredies, Dirk A. Lorenz, und Peter Maass
    Computational Optimization and Applications, 42(2):173-193, 2009
    [doi]
  34. On the convergence speed of iterative methods for linear inverse problems with sparsity constraints
    Kristian Bredies und Dirk A. Lorenz
    Journal of Physics: Conference Series 124:012031 (12pp), 2008
    [doi]
  35. Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
    Dirk A. Lorenz
    Journal of Inverse and Ill-Posed Problems, 16(5):463-478, 2008
    [doi, arXiv.org/abs/0801.1774]
  36. Optimal Convergence Rates for Tikhonov Regularization in Besov Scales
    Dirk A. Lorenz und Dennis Trede
    Inverse Problems 24(5):055010 (14pp), 2008
    [doi, arXiv.org/abs/0806.0951]
  37. Linear convergence of iterative soft-thresholding
    Kristian Bredies und Dirk A. Lorenz
    Journal of Fourier Analysis and Applications, 14(5-6):813-837, 2008
    [doi, arXiv.org/abs/0709.1598]
  38. A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints
    Roland Griesse und Dirk A. Lorenz
    Inverse Problems 24:035007 (19pp), 2008
    [doi, arXiv.org/abs/0709.3186]
    m-File mit ssn.m
  39. Iterated hard shrinkage for minimization problems with sparsity constraints
    Kristian Bredies und Dirk A. Lorenz
    SIAM Journal on Scientific Computing, 30(2):657-683, 2008
    [doi]
    m-File mit iter_thresh.m
  40. The Canonical Coherent States Associated With Quotients of the Affine Weyl-Heisenberg Group
    Stephan Dahlke, Dirk A. Lorenz, Peter Maass, Chen Sagiv und Gerd Teschke
    Journal of Applied Functional Analysis, 3(2):215-232, 2008
    [.pdf]
  41. Shrinkage versus Deconvolution
    Esther Klann, Michael Kuhn, Dirk A. Lorenz, Peter Maass und Herbert Thiele
    Inverse Problems, 23:2231-2248, 2007
    [doi]
  42. A Generalized Conditional Gradient Method for Non-Linear Operator Equations with Sparsity Constraints
    Kristian Bredies, Thomas Bonesky, Dirk A. Lorenz und Peter Maass
    Inverse Problems, 23:2041-2058, 2007
    [doi]
  43. Non-convex Variational Denoising of Images: Interpolation Between Hard and Soft Wavelet Shrinkage
    Dirk A. Lorenz
    Current Development in Theory and Applications of Wavelets, 1(1):31-56, 2007
  44. Solving Variational Problems in Image Processing via Projections - A Common View on TV Denoising and Wavelet Shrinkage
    Dirk A. Lorenz
    Zeitschrift für angewandte Mathematik und Mechanik, 81(1):247-256, 2007
    [doi]
  45. Mathematical Concepts of Multiscale Smoothing
    Kristian Brdies, Dirk A. Lorenz und Peter Maass
    Applied and Computational Harmonic Analysis, 19(2):141-161, 2005
    [doi]

Referierte Konferenzbeiträge

  1. Cartoon-Texture-Noise Decomposition with Transport Norms
    Christoph Brauer and Dirk A. Lorenz
    Proceedings of Scale Space and Variational Methods 2015, Lecture notes in Computer Science, Jean-François Aujol, Mila Nikolova, Nicolas Papadakis, (Eds.), 9087:142–153. Springer, 2015. [doi].
  2. A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing.
    Dirk A. Lorenz, Frank Schöpfer, Stephan Wenger, and Marcus Magnor. Pro- ceedings of ICIP 2014, March 2014.
    Recognized as one of the “Top 10%” papers. [doi, arXiv.org/abs/1403.7543]
  3. Variational methods for motion deblurring with still background
    Eileen Laue and Dirk A. Lorenz
    Proceedings of Scale Space and Variational Methods 2013, Lecture notes in Computer Science, Arjan Kuijper, Thomas Pock, Kristian Bredies, and Horst Bischof, (Eds.), 7893:74–85. Springer, 2013. [doi].
  4. Convergence to consensus by general averaging
    Dirk A. Lorenz und Jan Lorenz
    Positive Systems, Proceedings of POSTA 2009, Lecture Notes in Control and Information Sciences, Rafeal Bru, Sergion Romero-Vivo (Eds.), 389:91-100, 2009
  5. An active set approach to the elastic-net and its applications in mass spectrometry
    Theodore Alexandrov, Oliver Keszöcze, Dirk A. Lorenz, Stefan Schiffler, und Klaus Steinhorst
    Proceedings of SPARS09, 2009
  6. Greedy deconvolution of point-like objects
    Dirk A. Lorenz und Dennis Trede
    Proceedings of SPARS09, 2009
  7. Topology-preserving geodesic active contours for segmentation of high-content fluorescent cellular imaging
    Dirk A. Lorenz, Peter Maass, Hartwig Preckel und Dennis Trede
    PAMM, 8(1):10941-10942, 2009, Special Issue: 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Bremen 2008
    [doi]
  8. Iterated hard-thresholding for linear inverse problems with sparsity constriants
    Kristian Bredies und Dirk A. Lorenz
    PAMM, 7(1):2060061-2060062, 2007
    [doi]
  9. An optimal control problem in image processing
    Kristian Bredies, Dirk A. Lorenz, und Peter Maass
    PAMM, 6(1): 859-860, 2006
    [doi]
  10. On the minimization of non-convex, non-differentiable functionals with an application to SPECT
    Thomas Bonesky, Kristian Bredies, Dirk A. Lorenz, und Peter Maass
    In Oberwolfach Report: Mathematical Methods in Tomography34:18-22, 2006
  11. An Optimal Control Problem in Medical Image Processing
    Kristian Bredies, Dirk A. Lorenz, und Peter Maass
    In Systems, Control, Modeling and Optimization Proceedings of 22nd IFIP TC 7 Conference 249-26, 2006
  12. A Partial Differential Equation for Continuous Non-Linear Shrinkage Filtering and its Application for Analyzing MMG Data
    Kristian Bredies, Dirk A. Lorenz, Peter Maass, und Gerd Teschke
    In Photonics East, SPIE, 2003

Buchkapitel

  1. Wirkstoffe, Medikamente und Mathematische Bildverarbeitung
    Günther J. Bauer, Dirk A. Lorenz, Peter Maass, Hartwig Preckel, und Dennis Trede
    in acatech diskutiert, acatech - Deutsche Akademie der Technikwissenschaften, 2008
  2. Wissenschaftliches Rechnen im Tandem
    Dirk A. Lorenz
    in Jahrbuch den Universität Bremen, 2007
  3. Multiscale Approximation
    Stephan Dahlke, Peter Maass, Gerd Teschke, Karsten Koch, Dirk A. Lorenz, Stephan Müller, Stefan Schiffler, Andreas Stämpfli, Herbert Thiele, und Manuel Werner
    in Mathematical Methods in Time Series Analysis and Digital Image Processing, Springer, 2007

Abschlussarbeiten

  1. Wavelet Shrinkage in Signal and Image Processing - An Investigation of Relations and Equivalences
    Dirk A. Lorenz
    Dissertation, Universität Bremen, Februar 2005.
    [.pdf, published at elib at SuUB]
  2. Methoden der Multiskalenglättung
    Dirk A. Lorenz
    Diplomarbeit, Universität Bremen, August 2002.
    [.pdf]

Unveröffentlicht

  1. Nonlinear complex and cross diffusion
    Kristian Bredies, Dirk A. Lorenz, und Yehoshua Y. Zeevi, 2006
  2. A Comparison of Denoising Methods for One Dimensional Time Series
    Thoster Köhler und Dirk A. Lorenz, 2005
  3. Variational Denoising in Besov Spaces and Interpolation of Hard and Soft Wavelet Shrinkage
    Dirk A. Lorenz, 2004

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