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.
|Title of host publication||Proceedings of the 2003 International Conference on Image Processing|
|Publisher||Kluwer Academic Publishers|
|Publication status||Published - 2003|
|Event||2003 International Conference on Image Processing - |
Duration: 14 Sep 2003 → 17 Sep 2003
|Conference||2003 International Conference on Image Processing|
|Period||14/09/2003 → 17/09/2003|