On some deterministic dictionaries supporting sparsity

Shamgar Gurevich; Ronny Hadani; Nir Sochen

doi:10.1007/s00041-008-9043-z

On some deterministic dictionaries supporting sparsity

Shamgar Gurevich^*, Ronny Hadani, Nir Sochen

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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 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 language	English
Pages (from-to)	859-876
Number of pages	18
Journal	Journal of Fourier Analysis and Applications
Volume	14
Issue number	5-6
DOIs	https://doi.org/10.1007/s00041-008-9043-z
State	Published - Dec 2008

Keywords

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

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KW - Eigenfunctions

KW - Explicit algorithm

KW - Low coherence

KW - Sparsity

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On some deterministic dictionaries supporting sparsity

Abstract

Keywords

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