On Theorem 10 in "On Polar Polytopes and the Recovery of Sparse Representations" [Sep 07 3188-3195]

On Theorem 10 in "On Polar Polytopes and the Recovery of Sparse Representations" [Sep 07 3188-3195]

It is shown that Theorem 10 (Non-Nestedness of ERC) in [Plumbley, IEEE Trans. Inf. Theory, vol. 53, pp. 3188-3195, Sep. 2007] neglects the derivations of the exact recovery conditions (ERCs) of constrained l 1 -minimization (BP) and orthogonal matching pursuit. This means that it does not reflect th...

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Veröffentlicht in:IEEE transactions on information theory 2013-08, Vol.59 (8), p.5206-5209
Hauptverfasser: Sturm, Bob L., Mailhe, Boris, Plumbley, Mark D.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Basis pursuit
Compressed sensing
Computer Science
Engineering Sciences
Information theory
Iterative methods
Linear programming
Matching pursuit algorithms
orthogonal matching pursuit (OMP)
Signal and Image processing
sparse representation
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Zusammenfassung:It is shown that Theorem 10 (Non-Nestedness of ERC) in [Plumbley, IEEE Trans. Inf. Theory, vol. 53, pp. 3188-3195, Sep. 2007] neglects the derivations of the exact recovery conditions (ERCs) of constrained l 1 -minimization (BP) and orthogonal matching pursuit. 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. Inf. Theory, vol. 50, pp. 2231-2242, Oct. 2004] is shown.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2259294