Sparse decompositions in 'incoherent' dictionaries

R. Gribonval, Morten Nielsen

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearch

12 Citations (Scopus)


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 languageEnglish
Title of host publicationProceedings of the 2003 International Conference on Image Processing
PublisherKluwer Academic Publishers
Publication date2003
ISBN (Electronic)0-7803-7750-8
Publication statusPublished - 2003
Event2003 International Conference on Image Processing -
Duration: 14 Sep 200317 Sep 2003


Conference2003 International Conference on Image Processing


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