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The letter presents a method for the reduction in the mutual coherence of anovercomplete Gaussian or Bernoulli random matrix, which is fairly small due tothe lower bound given here on the probability of the event that the aforesaidmutual coherence is less than any given number in (0, 1). The mutual coherenceof the matrix that belongs to a set which contains the two types of matriceswith high probability can be reduced by a similar method but a subset that hasLebesgue measure zero. The numerical results are provided to illustrate thereduction in the mutual coherence of an overcomplete Gaussian, Bernoulli oruniform random dictionary. The effect on the third type is better than a formerresult.

Improved mutual coherence of some random overcomplete dictionaries for sparse repsentation