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 alleviating 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.

由于压缩感知使用一组减少的测量来处理信号重建，因此唯一解决方案的存在至关重要。解决这个问题的最重要的方法是基于计算上不可行的受限等距特性。基于一致性索引的唯一性标准在计算上是有效的，但是，它们是悲观的。最近引入了一种缓解此问题的方法，通过放宽使用正交匹配追踪方法进行唯一信号重建的相干指数条件。如果我们只考虑解的存在而不考虑其重建，则可以进一步放宽这种方法并改进稀疏界限。本文中使用 Gershgorin 圆盘定理推导出了一个这样的改进的稀疏限制界限。