Exact recovery analysis of non-negative orthogonal matching pursuit

Abstract : 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.
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Thi Thanh Nguyen, Charles Soussen, Jérôme Idier, El-Hadi Djermoune. Exact recovery analysis of non-negative orthogonal matching pursuit. Signal Processing with Adaptive Sparse Structured Representations Workshop, SPARS 2019, Jul 2019, Toulouse, France. ⟨hal-02378709⟩

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