On Some Deterministic Dictionaries Supporting Sparsity

被引：10

作者：

Gurevich, Shamgar ^{[1
]}

Hadani, Ronny ^{[2
]}

Sochen, Nir ^{[3
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[3] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2008年 / 14卷 / 5-6期

关键词：

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

D O I：

10.1007/s00041-008-9043-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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/root p. An explicit algorithm to construct a large portion of the oscillator dictionary is presented.

引用

页码：859 / 876

页数：18

共 19 条

[1]

[Anonymous], 1991, GRADUATE TEXTS MATH

[2]

Artin M., 1991, Algebra

[3]

BRUCKSTEIN AM, 2007, SIAM REV IN PRESS

[4] PAINLESS NONORTHOGONAL EXPANSIONS [J].

DAUBECHIES, I ;

GROSSMANN, A ;

MEYER, Y .

JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (05) :1271-1283

[5] Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization [J].

Donoho, DL ;

Elad, M .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2003, 100 (05) :2197-2202

[6] A generalized uncertainty principle and sparse representation in pairs of bases [J].

Elad, M ;

Bruckstein, AM .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (09) :2558-2567

[7]

Gilbert AC, 2003, SIAM PROC S, P243

[8]

Golomb S. W., 2005, SIGNAL DESIGN GOOD C

[9] Sparse representations in unions of bases [J].

Gribonval, R ;

Nielsen, M .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (12) :3320-3325

[10]

GUREVICH S, 2005, ARXIVMATH0612765

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