Title :
On sparse signal representations
Author :
Elad, Michael ; Bruckstein, Alfred M.
Author_Institution :
Jigami Res. Div., Jigami Corp., Haifa, Israel
fDate :
6/23/1905 12:00:00 AM
Abstract :
An elementary proof of a basic uncertainty principle concerning pairs of representations of ℛN 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;
Conference_Titel :
Image Processing, 2001. Proceedings. 2001 International Conference on
Conference_Location :
Thessaloniki
Print_ISBN :
0-7803-6725-1
DOI :
10.1109/ICIP.2001.958936
