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 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.