Incoherent frames design and dictionary learning using a distance barrier

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 im-prove both the representation error and the incoherence of the dictionary, compared with the standard approach.
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