L1TestPack: A software to generate test instances for l_1 minimization problems. L1TestPack consists of several Matlab m-files to generate test instances for the so-called Basis Pursuit Denoising problem (often referred to as BPDN) and to check several conditions related to these problems. While there are numerous solvers available, the purpose of this small package is to create instances which not only consist of the matrix A, the right hand side b and the parameter α but also with the corresponding solution x. To avoid ”inverse crimes” (i.e., just using some solver for the problem to generate an approximate solution), a different technique is used. The approach is, to start with a matrix A, a solution x and the parameter α and then calculate the corresponding b. One benefit of this approach is, that it is possible to choose the entries in x. Hence, L1TestPack is a helpful gadget for anyone who implements a BPDN-solver or who wants to create benchmarks for available solvers

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  1. Shehu, Yekini; Iyiola, Olaniyi S.; Ogbuisi, Ferdinard U.: Iterative method with inertial terms for nonexpansive mappings: applications to compressed sensing (2020)
  2. Lou, Yifei; Yan, Ming: Fast L1-L2 minimization via a proximal operator (2018)
  3. Friedlander, Michael P.; Goh, Gabriel: Efficient evaluation of scaled proximal operators (2017)
  4. Karimi, Sahar; Vavasis, Stephen: IMRO: A proximal quasi-Newton method for solving (\ell_1)-regularized least squares problems (2017)
  5. Fountoulakis, Kimon; Gondzio, Jacek: Performance of first- and second-order methods for (\ell_1)-regularized least squares problems (2016)
  6. Kruschel, Christian; Lorenz, Dirk A.: Computing and analyzing recoverable supports for sparse reconstruction (2015)
  7. Lorenz, Dirk A.; Pfetsch, Marc E.; Tillmann, Andreas M.: Solving basis pursuit: heuristic optimality check and solver comparison (2015)
  8. Zhang, Hui; Yin, Wotao; Cheng, Lizhi: Necessary and sufficient conditions of solution uniqueness in 1-norm minimization (2015)
  9. Ciak, R.; Shafei, B.; Steidl, G.: Homogeneous penalizers and constraints in convex image restoration (2013)
  10. Lorenz, Dirk A.: Constructing test instances for basis pursuit denoising (2013)
  11. Setzer, Simon; Steidl, Gabriele; Morgenthaler, Jan: A cyclic projected gradient method (2013)
  12. Becker, Stephen R.; Candès, Emmanuel J.; Grant, Michael C.: Templates for convex cone problems with applications to sparse signal recovery (2011)
  13. Lorenz, Dirk A.: Constructing test instances for basis pursuit denoising (2011) ioport