Research Group Optimization Andreas Tillmann
Dr. rer. nat.


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Research Group Optimization
Technische Universität Darmstadt
Dolivostraße 15
D-64293 Darmstadt

S4|10 26 (ground floor)

+49-6151-16-23453

tillmann@mathematik.tu-darmstadt.de

by appointment

I am a PostDoc at the Research Group Optimization (AG Optimierung) at TU Darmstadt.
In Winter 2014/15, I was an interim/visiting professor for mathematical optimization at TU Braunschweig; for lecture materials, see my website there.


Research Publications Software Conferences & Workshops Teaching Deutsche Versionflag

Research

My research interests focus on minimum-support solutions of underdetermined linear equation systems and other sparsity-related problems. I enjoy exploring both theoretical and practical aspects of optimization and complexity theory in areas like compressed sensing, signal and image processing, and machine learning.

From 2011 to 2013, I was supported by a research grant as part of the DFG project "SPEAR – Sparse Exact and Approximate Recovery", see the SPEAR Homepage.
I am currently affiliated with the project "EXPRESS – EXploiting structure in comPREssed Sensing using Side constraints" within the DFG priority program CoSIP ("Compressed Sensing in Information Processing", SPP 1798).

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Publications

  • A Primal-Dual Homotopy Algorithm for ℓ1-Minimization with ℓ-Constraints,
    with Christoph Brauer and Dirk A. Lorenz; submitted, October 2016. Preprint: Optimization Online E-Print ID 2016-10-5700, arXiv:1610.10022
    1-Houdini-Code for Matlab and test instances from the paper can be found here.
  • Sparse Recovery With Integrality Constraints,
    with Jan-Hendrik Lange, Bianca M. Seib and Marc E. Pfetsch; submitted, August 2016. Preprint: arXiv:1608.08678
  • DOLPHIn – Dictionary Learning for Phase Retrieval,
    with Yonina C. Eldar and Julien Mairal; IEEE Transactions on Signal Processing 64(24), 2016, pp. 6485–6500. DOI: 10.1109/TSP.2016.2607180 (Preprint: arXiv:1602.02263).
    DOLPHIn-Code for Matlab and test images from the paper as well as supplementary computational results can be found here.
  • Dictionary Learning from Phaseless Measurements,
    with Yonina C. Eldar and Julien Mairal; Proc. ICASSP 2016, pp. 4702–4706. DOI: 10.1109/ICASSP.2016.7472569.
  • Equivalence of Linear Programming and Basis Pursuit,
    PAMM (Proceedings in Applied Mathematics and Mechanics) 15(1), 2015, pp. 735–738. DOI: 10.1002/PAMM.201510351 (Preprint)
  • On the Computational Intractability of Exact and Approximate Dictionary Learning,
    IEEE Signal Processing Letters 22(1), 2015, pp. 45–49. DOI: 10.1109/LSP.2014.2345761 (Preprint: arXiv:1405.6664)
  • Computational Aspects of Compressed Sensing,
    Dissertation, TU Darmstadt, 2013. ISBN 978-3-8439-1445-1; electronic version: here
  • Projection Onto The Cosparse Set is NP-Hard,
    with Rémi Gribonval and Marc E. Pfetsch; Proc. ICASSP 2014, pp. 7148–7152. DOI: 10.1109/ICASSP.2014.6854987 (Preprint: arXiv:1303.5305, or HAL-00802359).
  • An Infeasible-Point Subgradient Method Using Adaptive Approximate Projections,
    with Dirk A. Lorenz and Marc E. Pfetsch; Computational Optimization and Applications 57(2), 2014, pp. 271–306. DOI: 10.1007/s10589-013-9602-3 (Preprint: Optimization Online E-Print ID 2011-04-3016, or arXiv:1104.5351)
  • Solving Basis Pursuit: Heuristic Optimality Check and Solver Comparison,
    with Dirk A. Lorenz and Marc E. Pfetsch; ACM Transactions on Mathematical Software 41(2), 2015, Art. No. 8. DOI: 10.1145/2689662 (Preprint: Optimization Online E-Print ID 2011-07-3100).
    Several accompanying software (HOC Suite, ISAL1, L1-Testset) can be found below. An overview of updated computational results (as of April 2016) is here.
  • The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing,
    with Marc E. Pfetsch; IEEE Transactions on Information Theory 60(2), 2014, pp. 1248–1259. DOI: 10.1109/TIT.2013.2290112 (Preprint: arXiv:1205.2081). A preliminary version achieved the Best Student Paper Award at SPARS'13.
  • Visualization of Astronomical Nebulae via Distributed Multi-GPU Compressed Sensing Tomography,
    with Stephan Wenger, Marco Ament, Stefan Guthe, Dirk A. Lorenz, Daniel Weiskopf and Marcus Magnor; IEEE Transactions on Visualization and Computer Graphics 18(12), 2012, pp. 2188–2197. DOI: 10.1109/TVCG.2012.281

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Software

  • HOC Suite
    Matlab package containing code for Heuristic Optimality Checks (HOCs) for Basis Pursuit, Basis Pursuit Denoising, and L1-Regularized Least-Squares. HOC can improve speed and accuracy of existing solvers for these problems (see README file for details, and results in "Solving Basis Pursuit" paper along with this HOC Demo for BP).
    (Version 1.0 of 09/30/2013).
  • ISAL1
    Matlab implementation of the Infeasible-Point Subgradient Algorithm for Basis Pursuit; also includes prototype code (ISAL1bpdn) for BP Denoising.
    (Version 1.00 of 09/30/2013 – current release; the "Solving Basis Pursuit" paper used Version 0.91 of 10/08/2012).
  • L1-Testset: ascii, mat
    The testset we used in our L1-solver comparison ("Solving Basis Pursuit" paper) as ascii- or Matlab binary files, accompanied by Matlab routines for data handling.
    (Size of zip-files: 313MB (ascii), 1GB (mat))
  • L1TestPack
    Matlab package by Dirk Lorenz for generating test instances for L1-minimization problems, to which I contributed.
    (Version 1.2 of 04/12/2012).
  • DOLPHIn
    Matlab implementation of the dictionary learning method for 2D noisy (sparse) phase retrieval.
    (Version 1.10 of 07/25/2016; requires SPAMS package), test images from the "DOLPHIn" paper are here, a document with lots of result tables of supplementary numerical experiments is here.
  • 1-Houdini
    Matlab-Code and test instances for our homotopy method for ℓ1-Minimization under ℓ-Norm-Constraints.
    (zip-file size: 152MB)

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Conferences and Workshops

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Teaching

Winter Term 2016/17

Summer Term 2016

Winter Term 2015/16

Summer Term 2015

Summer Term 2014

Winter Term 2013/14


(From my time at the TU Braunschweig, see old local homepage.)

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