Abstract
The purpose of this paper is to generalize a result by Donoho, Huo, Elad and Bruckstein on sparse representations of signals/images in a union of two orthonormal bases. We consider general (redundant) dictionaries in finite dimension, and derive sufficient conditions on a signal/image for having a unique sparse representation in such a dictionary. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of a combinatorial optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant. The special case where the dictionary is given by a union of several orthonormal bases is studied in more detail and some examples are given.
| Original language | English |
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| Title of host publication | Proceedings of the 2003 International Conference on Image Processing |
| Volume | 1 |
| Publisher | Kluwer Academic Publishers |
| Publication date | 2003 |
| Pages | 33-36 |
| ISBN (Electronic) | 0-7803-7750-8 |
| DOIs | |
| Publication status | Published - 2003 |
| Event | 2003 International Conference on Image Processing - Duration: 14 Sept 2003 → 17 Sept 2003 |
Conference
| Conference | 2003 International Conference on Image Processing |
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| Period | 14/09/2003 → 17/09/2003 |