  Since compressive sensing deals with a signal reconstruction using a reduced
set of measurements, the existence of a unique solution is of crucial
importance. The most important approach to this problem is based on the
restricted isometry property which is computationally unfeasible. The coherence
index-based uniqueness criteria are computationally efficient, however, they
are pessimistic. An approach to alleviate this problem has been recently
introduced by relaxing the coherence index condition for the unique signal
reconstruction using the orthogonal matching pursuit approach. This approach
can be further relaxed and the sparsity bound improved if we consider only the
solution existence rather than its reconstruction. One such improved bound for
the sparsity limit is derived in this paper using the Gershgorin disk theorem.
