  The construction of highly incoherent frames, sequences of vectors placed on
the unit hyper sphere of a finite dimensional Hilbert space with low
correlation between them, has proven very difficult. Algorithms proposed in the
past have focused in minimizing the absolute value off-diagonal entries of the
Gram matrix of these structures. Recently, a method based on convex
optimization that operates directly on the vectors of the frame has been shown
to produce promising results. This paper gives a detailed analysis of the
optimization problem at the heart of this approach and, based on these
insights, proposes a new method that substantially outperforms the initial
approach and all current methods in the literature for all types of frames,
with low and high redundancy. We give extensive experimental results that show
the effectiveness of the proposed method and its application to optimized
compressed sensing.
