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In this work, we study the links between the recovery properties of sparse signals for Orthogonal Matching Pursuit (OMP) and the whole General MP class over nested supports. We show that the optimality of those algorithms is not locally nested: there is a dictionary and supports I and J with J included in I such that OMP will recover all signals of support I, but not all signals of support J. We also...
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 -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...
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