  In sparse recovery, the unique sparsest solution to an under-determined
system of linear equations is of main interest. This scheme is commonly
proposed to be applied to signal acquisition. In most cases, the signals are
not sparse themselves, and therefore, they need to be sparsely represented with
the help of a so-called dictionary being specific to the corresponding signal
family. The dictionaries cannot be used for optimization of the resulting
under-determined system because they are fixed by the given signal family.
However, the measurement matrix is available for optimization and can be
adapted to the dictionary. Multiple properties of the resulting linear system
have been proposed which can be used as objective functions for optimization.
This paper discusses two of them which are both related to the coherence of
vectors. One property aims for having incoherent measurements, while the other
aims for insuring the successful reconstruction. In the following, the
influences of both criteria are compared with different reconstruction
approaches.
