Abstract
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 p 5 unit vectors in a Hilbert space of dimension p, whose pairwise inner products have magnitude of at most \(4/\sqrt{p}\) . An explicit algorithm to construct a large portion of the oscillator dictionary is presented.
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Communicated by Ronald A. DeVore.
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Gurevich, S., Hadani, R. & Sochen, N. On Some Deterministic Dictionaries Supporting Sparsity. J Fourier Anal Appl 14, 859–876 (2008). https://doi.org/10.1007/s00041-008-9043-z
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DOI: https://doi.org/10.1007/s00041-008-9043-z
Keywords
- Sparsity
- Deterministic dictionaries
- Low coherence
- Weil representation
- Commutative subgroups
- Eigenfunctions
- Explicit algorithm