Low Mutual and Average Coherence Dictionary Learning Using Convex Approximation

Abstract

In dictionary learning, a desirable property for the dictionary is to be of low mutual and average coherences. Mutual coherence is defined as the maximum absolute correlation between distinct atoms of the dictionary, whereas the average coherence is a measure of the average correlations. In this paper, we consider a dictionary learning problem regularized with the average coherence and constrained by an upper-bound on the mutual coherence of the dictionary. Our main contribution is then to propose an algorithm for solving the resulting problem based on convexly approximating the cost function over the dictionary. Experimental results demonstrate that the proposed approach has higher convergence rate and lower representation error (with a fixed sparsity parameter) than other methods, while yielding similar mutual and average coherence values.