Publications

Preprints

  • Damage Identification in Fiber Metal Laminates using Bayesian Analysis with Model Order Reduction
    Nanda Kishore Bellam Muralidhar, Carmen Gräßle, Natalie Rauter, Andrey Mikhaylenko, Rolf Lammering, Dirk A. Lorenz
    Eingereicht, Juni 2022
    [arxiv.org/abs/2206.04329]
  • Faster Randomized Block Sparse Kaczmarz by Averaging
    Lionel Tondji, Dirk A Lorenz
    Submitted, March 2022
    [arxiv.org/abs/2203.10838]
  • Lα -Regularization of the Beckmann Problem
    Dirk Lorenz, Hinrich Mahler and Christian Meyer
    Submitted, January 2022
    [arxiv.org/abs/2201.07086]
  • Chambolle-Pock's Primal-Dual Method with Mismatched Adjoint
    Dirk A. Lorenz and Felix Schneppe
    Submitted, January 2022
    [arxiv.org/abs/2201.04928]
  • Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition
    Andrea Ebner, Jürgen Frikel, Dirk Lorenz, Johannes Schwab, Markus Haltmeier
    Submitted, August 2020
    [arxiv.org/abs/2008.06219]
  • Primal-dual residual networks
    Christoph Brauer and Dirk Lorenz
    Submitted, June 2018
    [arXiv.org/abs/1806.05823].

 

Refereed Journal Publications

  • Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition
    Andrea Ebner, Jürgen Frikel, Dirk Lorenz, Johannes Schwab, Markus Haltmeier
    Applied and Computational Harmonic Analysis, 62:66-83 2023
    [doiarxiv.org/abs/2008.06219]
  • Extended Randomized Kaczmarz Method for Sparse Least Squares and Impulsive Noise Problems
    Frank Schöpfer, Dirk A Lorenz, Lionel Tondji, and Maximilian Winkler
    Lineare Algebra and Applications, 652:132-154, 2022
    [doiarxiv/abs/2201.08620]
  • Degenerate Preconditioned Proximal Point algorithms
    Kristian Bredies, Enis Chenchen, Dirk A. Lorenz, Emanuele Naldi
    To appear in SIAM Journal on Optimization
    [arxiv.org/abs/2109.11481]
  • Numerical Analysis of the Main Wave Propagation Characteristics in a Steel-CFRP Laminate Including Model Order Reduction
    Andrey Mikhaylenko, Natalie Rauter, Nanda Kishore Bellam Muralidhar, Tilmann Barth , Dirk A. Lorenz, and Rolf Lammering
    Acoustics, 4(3):517-537, 2022
    [doipreprints.org/manuscript/202206.0025]
  • Nonconvex flexible sparsity regularization: theory and monotone numerical schemes
    Daria Ghilli, Dirk A. Lorenz and Elena Resmerita
    Optimization, 71(4), 1117-1149, 2022
    [doi,arxiv]
  • Orlicz space regularization of continuous optimal transport problems
    Dirk A. Lorenz und Hinrich Mahler
    Applied Mathematics and Optimization, 85(14), 2022
    [doiarxiv.org/abs/2004.11574]
  • Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage
    Nanda Kishore Bellam Muralidhar, Natalie Rauter, Andrey Mikhaylenko, Rolf Lammering, Dirk A. Lorenz
    Modelling, Special Issue Simulation- and Modelling-Aided Structural Integrity and Safety, 2021
    [doi,preprints.org/manuscript/202109.0312]
  • Entropic regularization of continuous optimal transport problems
    Christian Clason, Dirk A. Lorenz, Hinrich Mahler und Benedikt Wirth
    Journal of Mathematical Analysis and Applications, 494(1), 2021
    [doi, arXiv.org/abs/1906.01333].
  • Quadratically regularized optimal transport
    Dirk A. Lorenz, Paul Manns und Christian Meyer
    Applied Mathematics and Optimization, 83 (3), 1919-1949, 2021
    [doi, arXiv.org/abs/1903.01112].
  • Complexity and Applications of the Homotopy Principle for Uniformly Constrained Sparse Minimization
    Christoph Brauer and Dirk A. Lorenz
    Applied Mathematics and Optimization, 82(3), 2020
    [doi]
  • Non-stationary Douglas-Rachford and alternating direction method of multipliers: adaptive stepsizes and convergence
    Dirk A. Lorenz and Quoc Tran-Dinh
    Computational Optimization and Applications, 74(1):67–92, 2019
    [doi, arXiv.org/abs/1801.03765].
  • Denoising of image gradients and total generalized variation denoising
    Birgit Komander, Dirk A. Lorenz, and Lena Vestweber
    Journal of Mathematical Imaging and Vision, 61(1):21-39, 2019
    [doi, arXiv.org/abs/1712.08585].
  • Linear convergence of the Randomized Sparse Kaczmarz method
    Frank Schöpfer and Dirk A. Lorenz
    Mathematical Programming, 173(1-2):509-536, 2019
    [doi, arXiv.org/abs/1610.02889].
    The is MATLAB code available as supplementary material at the Springer site. However, Springer made the files unusable, so, here is the code: MATLAB code for the randomized Kaczmarz method (zip, 64 KByte)
  • The randomized Kaczmarz Method with mismatched adjoint
    Dirk A. Lorenz, Sean Rose, and Frank Schöpfer
    BIT Numerical Mathematics 59(4):1079-1098, 2018
    [doi, arXiv.org/abs/1803.02848].
  • Sarrus Rules for Matrix Determinants and Dihedral Groups
    Dirk A. Lorenz and Karl-Joachim Wirths
    The College Mathematics Journal, 49(5):333-340, 2018.
    Reprinted: Mathematics Newsletter, 29(2):44-48, 2018
    [doi, arxiv.org/abs/1809.08948]
  • A Primal-Dual Homotopy Algorithm for ℓ1-Minimization with ℓ∞-Constraints
    Christoph Brauer, Dirk A. Lorenz, and Andreas M. Tillmann
    Computational Optimization and Applications, 70(2):443-478, 2018
    [doi, arXiv.org/abs/1610.10022, OO].
  • An extended Perona-Malik model based on probabilistic models
    Lars M. Mescheder and Dirk A. Lorenz
    Journal of Mathematical Imaging and Vision, 60(1):128-144, 2018
    [arXiv.org/abs/1612.06176].
  • How to be best in the OECD Better Life Index?
    Jan Lorenz, Christoph Brauer, and Dirk A. Lorenz
    Social Indicators Research, 134(1):75-92, 2017
    [doi, arXiv.org/abs/1608.04556]
  • Flexible sparse regularization
    Dirk A. Lorenz and Elena Resmerita
    Inverse Problems, 33(1), 2016
    [doi, arXiv.org/abs/1601.04429].
  • An inertial forward-backward method for monotone inclusions
    Dirk A. Lorenz and Thomas Pock
    Journal of Mathematical Imaging and Vision, 51(2):311-325, 2015
    [doi, arXiv.org/abs/1403.3522].
  • Computing and analyzing recoverable supports for sparse reconstruction
    Christian Kruschel and Dirk A. Lorenz
    Advances in Computational Mathematics, 41(6):1119-1144, 2015
    [doi, arXiv.org/abs/1309.2460].
  • Minimization of non-smooth, non-convex functionals by iterative thresholding
    Kristian Bredies, Dirk A. Lorenz and Stefan Reiterer
    Journal of Optimization Theory and Applications, 165(1),78-112, 2015
    [doi, DFG SPP 1324 Preprint 10]
  • Solving Basis Pursuit: Subgradient Algorithm, Heuristic Optimality Check, and Solver Comparison
    Dirk A. Lorenz, Marc E. Pfetsch and Andreas M. Tillmann
    ACM Transactions on Mathematical Software, 41(2), 2015
    [doi, OO Preprint].
  • Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized x-ray CT
    Jakob S. Jørgensen, Christian Kruschel and Dirk A. Lorenz
    Inverse Problems in Science and Engineering, 2014
    [doi, arXiv.org/abs/1409.0214].
  • 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].
  • Imaging with Kantorovich-Rubinstein discrepancy
    Jan Lellmann, Dirk A. Lorenz, Carola Schönlieb and Tuomo Valkonen
    SIAM Journal on Imaging Sciences, 7(4):2833-2859 2014
    [doi, arXiv.org/abs/1407.0221].
  • The linearized Bregman method via split feasibility problems
    Dirk A. Lorenz, Frank Schöpfer and Stephan Wenger
    SIAM Journal in Imaging Sciences, 7(2) 2014
    [doi, arXiv.org/abs/1309.2094].
  • 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, and Ingo Rustenbeck
    Microscopy and Microanalysis, 20(1):206-218, 2014
    [doi].
  • An Infeasible-Point Subgradient Method Using Adaptive Approximate Projections
    Dirk A. Lorenz, Marc E. Pfetsch and Andreas M. Tillmann
    Computational Optimization and Applications, 57(2):271-306, 2014
    [doi, arXiv.org/abs/1104.5351].
  • Fast image-based modeling of astronomic nebulae
    Stephan Wenger, Dirk A. Lorenz and Marcus Magnor
    Computer Graphics Forum, 32(7), 2013
    [doi].
  • Necessary conditions for variational regularization schemes
    Dirk A. Lorenz and Nadja Worliczek
    Inverse Problems, 20:075016pp, 2013
    [doi, arXiv.org/abs/1204.0649].
  • 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).
  • Visualization of astronomical nebulae via distributed multi-GPU compressed sensing tomography
    Stephan Wenger, Marco Ament, Stefan Guthe, Dirk A. Lorenz, Andreas Tillmann, Daniel Weiskopf, and Marcus Magnor
    IEEE Transactions on Visualization and Computer Graphics, 18(12):2188-2197, 2012.
    [doi]
  • 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 and Pham Q. Muoi
    Electronic Transactions on Numerical Analysis, 39:437-463, 2012.
  • Image Sequence Interpolation based on Optical Flow, Segmentation, and Optimal Control
    Kanglin Chen and Dirk A. Lorenz
    IEEE Transactions on Image processing, 21(3):1020-1030, 2012.
    [doi]
  • Morozov's principle for the augmented Lagrangian method applied to linear inverse problems
    Klaus Frick, Dirk A. Lorenz and Elena Resmerita
    SIAM Multiscale Modelling and Simulation, 9(4):1528-1548 2011
    [doi, arXiv.org/abs/1010.5181]
  • Beyond convergence rates: Exact inversion with Tikhonov regularization with sparsity constraints
    Dirk A. Lorenz, Stefan Schiffler and Dennis Trede
    Inverse Problems, 27:085009, 2011
    [doi, arXiv.org/abs/1001.3276]
  • Image sequence interpolation using optimal control
    Kanglin Chen and Dirk A. Lorenz
    Journal of Mathematical Imaging and Vision 41(3):222-238, 2011
    [doi, arXiv.org/abs/1008.0548]
  • 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]
  • 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]
  • 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
  • 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]
  • 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]
  • Elastic-Net Regularization: Error estimates and Active Set Methods
    Bangti Jin, Dirk A. Lorenz, and Stefan Schiffler
    Inverse Problems, 25(11):115022 (26pp), 2009
    [doi, arXiv.org/abs/0905.0796]
  • Greedy Solution of Ill-Posed Problems: Error Bounds and Exact Inversion
    Loic Denis, Dirk A. Lorenz, and Dennis Trede
    Inverse Problems, 25(11):115017 (24pp), 2009
    [doi, arXiv.org/abs/0904.0154]
  • Regularization with non-convex separable constraints
    Kristian Bredies, Dirk A. Lorenz
    Inverse Problems, 25(8):085011 (14pp), 2009
    [doi,SPP 1324 Preprint 11]
  • Optimal convergence rates for Tikhonov regularization in Besov scales
    Dirk A. Lorenz and Dennis Trede
    Journal of Inverse and Ill Posed Problems, 17(1):69-76, 2009
    [doi]
  • On the role of sparsity in inverse problems
    Dirk A. Lorenz
    Journal of Inverse and Ill-Posed Problems, 17(1):61-68, 2009
    [doi]
  • A generalized conditional gradient method and its connection to an iterative shrinkage method
    Kristian Bredies, Dirk A. Lorenz, and Peter Maass
    Computational Optimization and Applications, 42(2):173-193, 2009
    [doi]
  • On the convergence speed of iterative methods for linear inverse problems with sparsity constraints
    Kristian Bredies and Dirk A. Lorenz
    Journal of Physics: Conference Series 124:012031 (12pp), 2008
    [doi]
  • 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]
  • Optimal Convergence Rates for Tikhonov Regularization in Besov Scales
    Dirk A. Lorenz and Dennis Trede
    Inverse Problems 24(5):055010 (14pp), 2008
    [doi, arXiv.org/abs/0806.0951]
  • Linear convergence of iterative soft-thresholding
    Kristian Bredies and Dirk A. Lorenz
    Journal of Fourier Analysis and Applications, 14(5-6):813-837, 2008
    [doi, arXiv.org/abs/0709.1598]
  • A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints
    Roland Griesse and Dirk A. Lorenz
    Inverse Problems 24:035007 (19pp), 2008
    [doi, arXiv.org/abs/0709.3186]
    m-file with ssn.m
  • Iterated hard shrinkage for minimization problems with sparsity constraints
    Kristian Bredies and Dirk A. Lorenz
    SIAM Journal on Scientific Computing, 30(2):657-683, 2008
    [doi]
    m-file with iter_thresh.m
  • The Canonical Coherent States Associated With Quotients of the Affine Weyl-Heisenberg Group
    Stephan Dahlke, Dirk A. Lorenz, Peter Maass, Chen Sagiv, and Gerd Teschke
    Journal of Applied Functional Analysis, 3(2):215-232, 2008
    [.pdf]
  • Shrinkage versus Deconvolution
    Esther Klann, Michael Kuhn, Dirk A. Lorenz, Peter Maass, and Herbert Thiele
    Inverse Problems, 23:2231-2248, 2007
    [doi]
  • A Generalized Conditional Gradient Method for Non-Linear Operator Equations with Sparsity Constraints
    Kristian Bredies, Thomas Bonesky, Dirk A. Lorenz, and Peter Maass
    Inverse Problems, 23:2041-2058, 2007
    [doi]
  • 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
  • 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]
  • Mathematical Concepts of Multiscale Smoothing
    Kristian Brdies, Dirk A. Lorenz, and Peter Maass
    Applied and Computational Harmonic Analysis, 19(2):141-161, 2005
    [doi]

 

Refereed Conference Publications

  • A Model-Based Damage Identification using Guided Ultrasonic Wave Propagation in Fiber Metal Laminates
    Nanda Kishore Bellam Muradlidhar und Dirk A. Lorenz
    VI ECCOMAS Young Investigators Conference YIC2021, 2021
  • Orlicz-space regularization for optimal transport and algorithms for quadratic regularization
    Dirk A. Lorenz und Hinrich Mahler
    NeurIPS workshop "Optimal Transport in Machine Learning", 2020.
    [arXiv.org/abs/1909.06082]
  • Learning to Dequantize Speech Signals by Primal-dual Networks: an Approach for Acoustic Sensor Networks,
    Christoph Brauer, Christoph, Ziyue Zhao, Dirk Lorenz, and Tim Fingscheidt.
    ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2019.
    [doi]
  • A Sinkhorn-Newton method for entropic optimal transport
    Christoph Brauer, Christian Clason, Dirk A. Lorenz und Benedikt Wirth
    NIPS Workshop "Optimal Transport in Machine Learning", 2017
    [arXiv.org/abs/1710.06635].
  • Denoising of image gradients and constrained total generalized variation
    Birgit Komander and Dirk A. Lorenz
    Proceedings of Scale Space and Variational Methods 2017, Lecture notes in Computer Science, Lauze F., Dong Y., Dahl A. (Eds.), 10302:435-446. Springer, 2017. [doi].
  • Sparse reconstruction of quantized speech signals,
    Brauer, Christoph, Timo Gerkmann, and Dirk Lorenz. 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. [doi]
  • 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].
  • A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing.
    Dirk A. Lorenz, Frank Schöpfer, Stephan Wenger, and Marcus Magnor. Proceedings of ICIP 2014, March 2014.
    Recognized as one of the "Top 10%" papers. [doi, arXiv.org/abs/1403.7543]
  • 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].
  • Convergence to consensus by general averaging
    Dirk A. Lorenz and 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
  • An active set approach to the elastic-net and its applications in mass spectrometry
    by Theodore Alexandrov, Oliver Keszöcze, Dirk A. Lorenz, Stefan Schiffler, and Klaus Steinhorst
    Proceedings of SPARS09, 2009
  • Greedy deconvolution of point-like objects
    by Dirk A. Lorenz and Dennis Trede
    Proceedings of SPARS09, 2009
  • Topology-preserving geodesic active contours for segmentation of high-content fluorescent cellular imaging
    by Dirk A. Lorenz, Peter Maass, Hartwig Preckel and 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]
  • Iterated hard-thresholding for linear inverse problems with sparsity constriants
    by Kristian Bredies and Dirk A. Lorenz
    PAMM, 7(1):2060061-2060062, 2007
    [doi]
  • An optimal control problem in image processing
    by Kristian Bredies, Dirk A. Lorenz, and Peter Maass
    PAMM, 6(1): 859-860, 2006
    [doi]
  • On the minimization of non-convex, non-differentiable functionals with an application to SPECT
    by Thomas Bonesky, Kristian Bredies, Dirk A. Lorenz, and Peter Maass
    In Oberwolfach Report: Mathematical Methods in Tomography34:18-22, 2006
  • An Optimal Control Problem in Medical Image Processing
    by Kristian Bredies, Dirk A. Lorenz, and Peter Maass
    In Systems, Control, Modeling and Optimization Proceedings of 22nd IFIP TC 7 Conference 249-26, 2006
  • A Partial Differential Equation for Continuous Non-Linear Shrinkage Filtering and its Application for Analyzing MMG Data
    by Kristian Bredies, Dirk A. Lorenz, Peter Maass, and Gerd Teschke
    In Photonics East, SPIE, 2003

 

Book chapter

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

Theses

      1. Wavelet Shrinkage in Signal and Image Processing - An Investigation of Relations and Equivalences
        by Dirk A. Lorenz
        PhD Thesis, Universität Bremen, February 2005.
        [.pdf, published at elib at SuUB]
      2. Methoden der Multiskalenglättung
        by Dirk A. Lorenz
        Diploma Thesis, Universität Bremen, August 2002.
        [.ps]

Unpublished

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