Sparse representations in unions of bases
نویسندگان
چکیده
The purpose of this correspondence is to generalize a result by Donoho and Huo and Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases for . We consider general (redundant) dictionaries for , and derive sufficient conditions for having uniquesparserepresentations of signals insuchdictionaries.Thespecial case where the dictionary is given by the union of 2 orthonormal bases for isstudiedinmoredetail.Inparticular,itisprovedthattheresultofDonoho and Huo, concerning the replacement of the optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant.
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عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 49 شماره
صفحات -
تاریخ انتشار 2003