  Within the Compressive Sensing (CS) paradigm, sparse signals can be
reconstructed based on a reduced set of measurements. Reliability of the
solution is determined by the uniqueness condition. With its mathematically
tractable and feasible calculation, coherence index is one of very few CS
metrics with a considerable practical importance. In this paper, we propose an
improvement of the coherence based uniqueness relation for the matching pursuit
algorithms. Starting from a simple and intuitive derivation of the standard
uniqueness condition based on the coherence index, we derive a less
conservative coherence index-based lower bound for signal sparsity. The results
are generalized to the uniqueness condition of the $l_0$-norm minimization for
a signal represented in two orthonormal bases.
