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On Theorem 10 in "On Polar Polytopes and the Recovery of Sparse Representations"

Bob Sturm 1 Boris Mailhé 2 Mark Plumbley 2
1 Department of Architecture and Design [Aalborg]
2 Centre for Digital Music, Queen Mary University of London
Centre for Digital Music
Abstract : It is shown that Theorem 10 (Non-Nestedness of ERC) in [Plumbley, IEEE Trans. Info. Theory, vol. 53, pp. 3188, Sep. 2007] neglects the derivations of the exact recovery conditions (ERCs) of constrained 1-minimization (BP) and orthogonal matching pursuit (OMP). This means that it does not reflect the recovery properties of these algorithms. Furthermore, an ERC of BP more general than that in [Tropp, IEEE Trans. Info. Theory, vol. 50, pp. 2231, Oct. 2004] is shown.
Keywords : Exact recovery condition basis pursuit orthog- onal matching pursuit
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Bob Sturm, Boris Mailhé, Mark Plumbley. On Theorem 10 in "On Polar Polytopes and the Recovery of Sparse Representations". IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2013, ⟨10.1109/TIT.2013.2259294⟩. ⟨hal-00839327⟩

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