Publications
Papers:


An InfeasiblePoint Subgradient Method Using Adaptive Approximate Projections
Dirk A. Lorenz, Marc E. Pfetsch, and Andreas M. Tillmann.
Computational Optimization and Applications 57(2), 2014, pp. 271–306,
DOI 10.1007/s1058901396023

Constructing test instances for Basis Pursuit Denoising
Dirk A. Lorenz.
IEEE Transactions on Signal Processing 61(5), 2013, pp. 1210–1214.
DOI 10.1109/TSP.2012.2236322
Code to reproduce the figures is here.

Solving Basis Pursuit: Heuristic Optimality Check and Solver Comparison
Dirk A. Lorenz, Marc E. Pfetsch, and Andreas M. Tillmann.
To appear in ACM Transactions on Mathematical Software, 2014.
Optimization Online EPrint ID 2011073100
A detailed table of numerical results can be found here.
A list of the test set instances is here.
Code to produce figures and tables, and result data files are here; see also this HOC Demo (cf. Fig. 10).

The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing
Marc E. Pfetsch and Andreas M. Tillmann.
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 MultiGPU Compressed Sensing Tomography
Stephan Wenger, Marco Ament, Stefan Guthe, Dirk A. Lorenz, Andreas M. Tillmann, Daniel Weiskopf, and Marcus Magnor.
IEEE Transactions on Visualization and Computer Graphics 18(12), 2012, pp. 2188–2197.
DOI 10.1109/TVCG.2012.281

Projection Onto The Cosparse Set is NPhard
Andreas M. Tillmann, Rémi Gribonval, and Marc E. Pfetsch.
Proceedings of ICASSP 2014, pp. 7148–7152. DOI 10.1109/ICASSP.2014.6854987

Computing and Analyzing Recoverable Supports for Sparse Reconstruction
Christian Kruschel and Dirk A. Lorenz. Submitted. September 2013.
arXiv:1309.2460
Code to reproduce the figures is here.


Talks & Presentations:


Geometrical Insights To Sparse Recovery via Minimally Redundant Matrices
Christian Kruschel. AIP 13 (Advances in Mathematical Image Processing), 09/30  02/10/2013 @ Annweiler, Germany.

The Computational Complexity of Spark, RIP, and NSP
Andreas M. Tillmann. SPARS 13 (Signal Processing with Adaptive Sparse Structured Representations), 07/08  07/11/2013 @ Lausanne, Switzerland. Best Student Paper Award
The slides can be found here.

Heuristic Optimality Check and Computational Solver Comparison for Basis Pursuit
Andreas M. Tillmann. ISMP 2012 (21st International Symposium on Mathematical Programming), 08/19  08/24/2012 @ Berlin, Germany.
The slides can be found here.

Solving Basis Pursuit
Andreas M. Tillmann. SIAM LA12 (SIAM Conference on Applied Linear Algebra), 06/18  06/22/2012 @ Valencia, Spain.
The slides can be found here.

Constructing Test Instances With Prescribed Properties for Sparsity Problems
Christian Kruschel. SIAM LA12 (SIAM Conference on Applied Linear Algebra), 06/18  06/22/2012 @ Valencia, Spain.

Branch & Cut for L0Minimization
Andreas M. Tillmann. Matheon Workshop (Sparse Representation of Functions: Analytic and Computational Aspects), 12/10  12/14/2012 @ Berlin, Germany.
The slides can be found here.

Constructing Test Instances for Sparse Recovery Algorithms
Christian Kruschel. SIAM IS12 (SIAM Conference on Imaging Science), 05/20  05/22/2012 @ Philadelphia, PA, USA.
The slides can be found here.

Basis pursuit denoising: Exact test instances and exact recovery for illposed problems
Dirk A. Lorenz. Dagstuhl Workshop on Sparse Representations and Efficient Sensing of Data, 01/30  02/04/2011 @ Schloss Dagstuhl, Germany.
The slides can be found here.

An InfeasiblePoint Subgradient Method and Computational Comparison for l1Minimization
Andreas M. Tillmann. CSSIP10 (Workshop on Compressed Sensing, Sparsity and Inverse Problems), 09/06  09/07/2010 @ TU Braunschweig, Germany.

An InfeasiblePoint Subgradient Method Using Approximate Projections
Andreas M. Tillmann. SIAM OP11 (SIAM Conference on Optimization), 05/16  05/19/2011 @ Darmstadtium, Darmstadt, Germany.
The poster can be found here.

An InfeasiblePoint Subgradient Algorithm and a Computational Solver Comparison for l1Minimization
Andreas M. Tillmann. SPARS 11 (Signal Processing with Adaptive Sparse Structured Representations), 06/27  06/30/2011 @ RCPE Edinburgh, UK.
The poster can be found here.


Software
L1 Test Pack 
A Matlab package to generate test instances for L1minimization problems (Version 1.2 of 04/12/2012).

find_sign_pattern 
A Matlab program that, given a matrix and sparsity level, computes a support and sign pattern such that any vector conforming to these is a unique Basis Pursuit solution.

HOC Suite 
A Matlab package containing code for Heuristic Optimality Checks (HOCs) for Basis Pursuit, Basis Pursuit Denoising, and L1Regularized LeastSquares. 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 
A Matlab implementation of the InfeasiblePoint Subgradient Algorithm for Basis Pursuit; the latest version includes prototype code (ISAL1bpdn) for BP Denoising as well. (Version 1.00 of 09/30/2013 — current release) (The "Solving Basis Pursuit" paper used Version 0.91 of 10/08/2012). 
L1Testset (ascii) 
The testset we used in our L1solver comparison as asciifiles, accompanied by Matlab routines for data handling. (Size of zipfile: 313MB) 
L1Testset (mat) 
The testset we used in our L1solver comparison as Matlab binary files. (Size of zipfile: 1GB) 
 
