Sparse representations in unions of bases
Top Cited Papers
- 1 December 2003
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 49 (12), 3320-3325
- https://doi.org/10.1109/tit.2003.820031
Abstract
The purpose of this correspondence is to generalize a result by Donoho and Huo and Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases for R/sup N/. We consider general (redundant) dictionaries for R/sup N/, and derive sufficient conditions for having unique sparse representations of signals in such dictionaries. The special case where the dictionary is given by the union of L/spl ges/2 orthonormal bases for R/sup N/ is studied in more detail. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of the /spl lscr//sup 0/ optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant.Keywords
This publication has 6 references indexed in Scilit:
- Grassmannian frames with applications to coding and communicationApplied and Computational Harmonic Analysis, 2003
- On sparse representation in pairs of basesIEEE Transactions on Information Theory, 2003
- Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ 1 minimizationProceedings of the National Academy of Sciences of the United States of America, 2003
- A generalized uncertainty principle and sparse representation in pairs of basesIEEE Transactions on Information Theory, 2002
- Uncertainty principles and ideal atomic decompositionIEEE Transactions on Information Theory, 2001
- Z4 -Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-SetsProceedings of the London Mathematical Society, 1997