On sparse signal representations

Author

Elad, Michael ; Bruckstein, Alfred M.

Author_Institution

Jigami Res. Div., Jigami Corp., Haifa, Israel

Volume

1

fYear

2001

fDate

6/23/1905 12:00:00 AM

Firstpage

3

Abstract

An elementary proof of a basic uncertainty principle concerning pairs of representations of ℛ^N vectors in different orthonormal bases is provided. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries. The main contribution in this paper is the improvement of an important result due to Donoho and Huo (1999) concerning the replacement of the l₀ optimization problem by a linear programming minimization when searching for the unique sparse representation

Keywords

linear programming; minimisation; signal representation; linear programming minimization; optimization problem; orthonormal bases; overcomplete dictionaries; sparse representation; uncertainty principle; unique sparse representation search; uniqueness property; vectors; Cities and towns; Computer science; Dictionaries; Equations; Linear programming; Signal generators; Signal processing; Signal representations; Uncertainty; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Image Processing, 2001. Proceedings. 2001 International Conference on

Conference_Location

Thessaloniki

Print_ISBN

0-7803-6725-1

Type

conf

DOI

10.1109/ICIP.2001.958936

Filename

958936