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Dictionary learning of convolved signals

Abstract : Assuming that a set of source signals is sparsely representable in a given dictionary, we show how their sparse recovery fails whenever we can only measure a convolved observation of them. Starting from this motivation, we develop a block coordinate descent method which aims to learn a convolved dictionary and provide a sparse representation of the observed signals with small residual norm. We compare the proposed approach to the K-SVD dictionary learning algorithm and show through numerical experiment on synthetic signals that, provided some conditions on the problem data, our technique converges in a fixed number of iterations to a sparse representation with smaller residual norm.
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https://hal.inria.fr/hal-00705998
Contributor : Jules Espiau De Lamaestre Connect in order to contact the contributor
Submitted on : Friday, June 8, 2012 - 4:15:26 PM
Last modification on : Monday, October 13, 2014 - 3:43:25 PM

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Daniele Barchiesi, Mark D. Plumbley. Dictionary learning of convolved signals. Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, May 2011, Praha, Czech Republic. pp.5812 -5815, ⟨10.1109/ICASSP.2011.5947682⟩. ⟨hal-00705998⟩

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