Incoherent frames design and dictionary learning using a distance barrier

•Combining quadratic term and distance barrier allows better design of incoherent frames.•Same function can be used for promoting incoherence in frame design and dictionary learning.•Top mutual coherence results are obtained in frames design.•In dictionary learning, both representation error and dictionary coherence can be improved with respect to standard algorithms. We present a unitary approach to the design of incoherent frames and to dictionary learning, by using a single function that promotes incoherence for both problems. This function has a context-dependent quadratic term and a distance barrier term that was never used in this context. We provide simple and efficient algorithms for both problems. Numerical results show that we can obtain large frames whose incoherence is better than of those designed by other methods. Also, in dictionary learning, we can improve both the representation error and the incoherence of the dictionary, compared with the standard approach.