Dictionary learning with low mutual coherence constraint

Abstract This paper presents efficient algorithms for learning low-coherence dictionaries. First, a new algorithm based on proximal methods is proposed to solve the dictionary learning (DL) problem regularized with the mutual coherence of dictionary. This is unlike the previous approaches that solve a regularized problem where an approximate incoherence promoting term, instead of the mutual coherence, is used to encourage low-coherency. Then, a new solver is proposed for constrained low-coherence DL problem, i.e., a DL problem with an explicit constraint on the mutual coherence of the dictionary. As opposed to current methods, which follow a suboptimal two-step approach, the new algorithm directly solves the associated DL problem. Using previous studies, convergence of the new schemes to critical points of the associated cost functions is also provided. Furthermore, it is shown that the proposed algorithms have lower iteration complexity than existing algorithms. Our simulation results on learning low-coherence dictionaries for natural image patches as well as image classification based on discriminative over-complete dictionary learning demonstrate the superiority of the proposed algorithms compared with the state-of-the-art method.