Research

Research areas

• Sparse representations in inverse problems and image processing
• Optimization and optimal control and its applications in inverse problems and image processing
• Nonlinear methods in image processing
• Applications in engineering and life sciences
• Variational analysis
  • Subgradients, subgradient descents
  • Nonlinear projections

Publications

My list of publications is not longer maintained here. Please refer to the page at TU Braunschweig: http://www.tu-braunschweig.de/iaa/personal/lorenz.

Talks

• Sparsity Constraints in Image Processing - Algorithms and Stability
  Talk at German-Israel Workshop for Vision and Image Sciences, Technion, Haifa, Israel, November 2008
  
• Non-convex regularization
  Talk at Chemnitz Symposium on Inverse Problems, Chemnitz, September 2008
  
• Inverse problems with sparsity constraints - Semismooth Newton methods and convergence rates
  Talk at DMV Jahrestagung, Erlangen, September 2008
  
• Semismooth Newton and active set methods for sparse reconstruction
  Talk at the SIAM Conference on Imaging Science, San Diego, USA, July 2008
  Slides: .pdf
• A semismooth Newton method for inverse problems with sparsity constraints
  Talk at the 5th European Congress on Computational Methods in Applied Sciences and Engineering, Venice, Italy, July 2008
  
• On the role of sparsity in inverse problems
  Talk at Inverse Problems: Modeling and Simulation, Fethiye, Turkey, May 2008
  
• On semismooth Newton methods for sparsity constraints
  Talk at the GAMM Annual Meeting, Bremen, March 2008
  
• Inverse problems with sparsity constraints
  Talk at the Computational Analysis Seminar, Jacobs University, Bremen, March 2008
  
• Is sparsity regularizing?
  Talk at the Chemnitz Symposium on Inverse Problems, Chemnitz, September 2007
  
• Shrinkage and projection methods for denoising and deblurring of images
  Talk at the 13th Czech-French-German Conference on Optimization, Heidelberg, September 2007
  
• Iterated hard shrinkage for linear inverse problems with sparsity constraints
  Talk at the ICIAM 2007, Zurich, July 2007
• On the convergence speed of iterative methods for linear inverse problems with sparsity constraints
  Talk at the Applied Inverse Problems 2007, Vancouver, June 2007
  Slides: .pdf
• On Generalized Gradient Methods for Non-differentiable Functionals - Application to Tikhonov Functionals with Sparsity Constraints
  Talk at the group seminar Optimization and Optimal Control, RICAM, Linz, February 2007
  Slides: .pdf
• Geometrische Topologie - Wer Brötchen gerecht teilen kann, kann auch Igel Kämmen (in German)
  Talk at the Workgroup Seminar 2007, Uttendorf, February 2007
  Slides: .pdf
• Nonlinear complex and cross diffusion for texture preserving denoising
  Talk at the HASSIP workshop "Multiscale Methods, Sparse Decompositions and Parsimonious Statistics", Munich, September 2006
  Slides: .pdf
• Die Dynamik des Konsens (in German)
  Talk at the Workgroup Seminar 2006, Uttendorf, February 2006
  Slides: .pdf
• Optimal Control Problems With Sparsity Contraints in Image Processing
  Talk at Recent Progress in Wavelet Analysis and Frame Theory, Bremen, January 2006
  Slides: .pdf
• Optimal Control of PDEs Applied in Image Processing - Analysis of a Generalized Conditional Gradient Method
  Talk at the Applied Math Seminar, Tel Aviv University, November 2005
  Slides: .pdf (movies not working…)
• Wieso Wavelet Shrinkage? Motivation und Anwendung (in German)
  Talk at the Oberseminar Rhein-Ruhr, Duisburg, November 2005
  Slides: .pdf
• A Control Problem in Medical Image Processing - Analysis of a Generalized Conditional Gradient Method
  Talk at the 22nd IFIP TC 7 Conference on System Modelling and Optimization, Turin, July 2005
  Slides: .pdf (movies not working…)
• Wavelet Shrinkage in Signal and Image Processing - A Mathematical Investigation of Relations and Equivalences
  Talk at the CeVis Oberseminar, Bremen, April 2005
  Slides: .pdf
• Schlüsselqualifikation Präsentieren - Vortragen von Mathematik mit der Beamer-Klasse (in German)
  Talk at the Workgroup Seminar 2005 Uttendorf, February 2005
  Slides: .pdf
• Mathematical Analysis of Different Denoising Methods - Interpolation between soft and hard wavelet shrinkage
  Talk at the Annual Meeting of DFG SPP 1114, Etelsen, September 2004
  Slides: .pdf
• R, dx and epsilon, Derivatives and Infinitesimal Numbers
  Talk at the Workgroup-Seminars 2004, Uttendorf, February 2004
  Slides: .pdf
• Shrinkage Methods and PDEs
  Talk at the workshop "Wavelets and Image Processing", Dortmund, April 2003
  Slides: .pdf
• Partielle Differentialgleichungen in der Bildverarbeitung (in German)
  Talk at the Workgroup-Seminar 2003, Uttendorf, February 2003
  Handout: .pdf, Slides: .pdf