Average performance of Orthogonal Matching Pursuit (OMP) for sparse approximation
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We present a theoretical analysis of the average performance of OMP for sparse approximation. For signals, that are generated from a dictionary with K atoms and coherence μ and coefficients corresponding to a geometric sequence with parameter α, we show that OMP is successful with high probability as long as the sparsity level S scales as Sμ^2 K ≲ 1-α . This improves by an order of magnitude over worst case results and shows that OMP and its famous competitor Basis Pursuit outperform each other depending on the setting.
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