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 \(\ell_1\)-minimization (BP) and orthogonal matching pursuit (OMP), and thus 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.
I E E E Transactions on Information Theory, 2013, Vol 59, Issue 8, p. 5206-5209