On some deterministic dictionaries supporting sparsity

Shamgar Gurevich*, Ronny Hadani, Nir Sochen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We describe a new construction of an incoherent dictionary, referred to as the oscillator dictionary, which is based on considerations in the representation theory of finite groups. The oscillator dictionary consists of approximately p5 unit vectors in a Hilbert space of dimension p, whose pairwise inner products have magnitude of at most 4/√p. An explicit algorithm to construct a large portion of the oscillator dictionary is presented.

Original languageEnglish
Pages (from-to)859-876
Number of pages18
JournalJournal of Fourier Analysis and Applications
Issue number5-6
StatePublished - Dec 2008


  • Commutative subgroups
  • Deterministic dictionaries
  • Eigenfunctions
  • Explicit algorithm
  • Low coherence
  • Sparsity
  • Weil representation


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