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ICML
2010
IEEE

Submodular Dictionary Selection for Sparse Representation

8 years 11 months ago
Submodular Dictionary Selection for Sparse Representation
We develop an efficient learning framework to construct signal dictionaries for sparse representation by selecting the dictionary columns from multiple candidate bases. By sparse, we mean that only a few dictionary elements, compared to the ambient signal dimension, can exactly represent or well-approximate the signals of interest. We formulate both the selection of the dictionary columns and the sparse representation of signals as a joint combinatorial optimization problem. The proposed combinatorial objective maximizes variance reduction over the set of training signals by constraining the size of the dictionary as well as the number of dictionary columns that can be used to represent each signal. We show that if the available dictionary column vectors are incoherent, our objective function satisfies approximate submodularity. We exploit this property to develop SDSOMP and SDSMA, two greedy algorithms with approximation guarantees. We also describe how our learning framework enables...
Andreas Krause, Volkan Cevher
Added 09 Nov 2010
Updated 09 Nov 2010
Type Conference
Year 2010
Where ICML
Authors Andreas Krause, Volkan Cevher
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