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.
翻译:由于压缩感应涉及使用一套减少的测量方法进行信号重建,因此存在一种独特的解决办法至关重要,这一问题最重要的办法是基于有限的等量性属性,这是无法计算出来的。但基于一致性指数的独特性标准在计算上是有效的,但这些标准是悲观的。最近采用了一种缓解这一问题的办法,即采用正方形对齐追踪方法,放松独特信号重建的一致性指数条件。如果我们只考虑解决办法的存在,而不是重建,这种办法可以进一步放松,宽度约束可以改善。本文用Gershgorin磁盘的理论来推断出对聚度限制的这种改进。