000175456 001__ 175456
000175456 005__ 20190430065056.0
000175456 0247_ $$2doi$$a10.1109/JSTSP.2011.2161862
000175456 022__ $$a1932-4553
000175456 02470 $$a000294012200009
000175456 037__ $$aARTICLE
000175456 245__ $$aGreedy Dictionary Selection for Sparse Representation
000175456 269__ $$a2011
000175456 260__ $$c2011
000175456 336__ $$aJournal Articles
000175456 520__ $$aWe 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 dictionary selection for structured sparse representations, e.g., where the sparse coefficients occur in restricted patterns. We evaluate our approach on synthetic signals and natural images for representation and inpainting problems.
000175456 6531_ $$adictionary selection
000175456 6531_ $$asubmodular optimization
000175456 6531_ $$adictionary learning
000175456 700__ $$0243957$$g199128$$aCevher, Volkan
000175456 700__ $$aKrause, Andreas
000175456 773__ $$j5$$tIEEE Journal of Selected Topics in Signal Processing$$k5$$q979-988
000175456 8564_ $$uhttps://infoscience.epfl.ch/record/175456/files/sp-dictionary.pdf$$zPostprint$$s5105260$$yPostprint
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000175456 917Z8 $$x199128
000175456 917Z8 $$x231598
000175456 937__ $$aEPFL-ARTICLE-175456
000175456 973__ $$rNON-REVIEWED$$sPUBLISHED$$aEPFL
000175456 980__ $$aARTICLE