Lossless Expanders in Compressive Sensing

  • Simon Foucart
  • Holger Rauhut
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


A new class of measurement matrices is introduced in this chapter. It consists of adjacency matrices of certain left regular bipartite graphs called lossless expanders. After pointing out basic properties of lossless expanders, their existence is established using probabilistic methods. The adjacency matrices are then proved to satisfy the null space property, hence enable sparse recovery via basis pursuit. Sparse recovery is also shown to be achieved via a variation of iterative hard thresholding. Finally, a rudimentary example of another type of algorithms that run in sublinear time is presented.


bipartite graph sdjacency matrix 1-minimization thresholding-based algorithm sublinear-time algorithm 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Simon Foucart
    • 1
  • Holger Rauhut
    • 2
  1. 1.Department of MathematicsDrexel UniversityPhiladelphiaUSA
  2. 2.Lehrstuhl C für Mathematik (Analysis)RWTH Aachen UniversityAachenGermany

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