Exact recovery analysis of non-negative orthogonal greedy algorithms
Résumé
It is well-known that Orthogonal Matching Pursuit (OMP) recovers the exact support of K-sparse signals under the condition μ < 1/(2K − 1) where μ denotes the mutual coherence of the dictionary. In this communication, we show that under the same condition and if the unknown K-sparse signal is non-negative, the weights of the atoms selected by OMP are non-negative at any of the first K iterations. Therefore, the generalized version of OMP to the non-negative setting (NNOMP) identifies with OMP, which allows us to establish an exact recovery analysis of NNOMP under the mutual coherence condition. We further establish a similar analysis of the non-negative extension of Orthogonal Least Squares (OLS), and discuss open issues related to the elaboration of weakened guarantees as compared to mutual coherence guarantees.
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