  Optimizing the acquisition matrix is useful for compressed sensing of signals
that are sparse in overcomplete dictionaries, because the acquisition matrix
can be adapted to the particular correlations of the dictionary atoms. In this
paper a novel formulation of the optimization problem is proposed, in the form
of a rank-constrained nearest correlation matrix problem. Furthermore,
improvements for three existing optimization algorithms are introduced, which
are shown to be particular instances of the proposed formulation. Simulation
results show notable improvements and superior robustness in sparse signal
recovery.
