Influence of Gibbs phenomenon on the mutual coherence in sparse representations

Abstract

The influence of ringing effect (which is based on the Gibbs phenomenon) on the mutual coherence in sparse representation approach is considered. It is shown that for random vectors, the ringing effect increases the average mutual coherence. Numerical results that demonstrate that the mutual coherence behaves identically for real images are given. It is also shown how the ringing effect affects the sparsity of representations (which is closely related to the mutual coherence).