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在压缩感知理论(CS)中,感知矩阵是否符合RIP准则直接决定了重构信号质量的好坏。实际应用中,如果感知矩阵不符合RIP准则,那么重构出的信号会因为误差太大而根本无法使用。因此,感知矩阵满足有限等距准则(RIP)是CS中的几个基本原则之一。本文首先对压缩感知理论进行了简要的回顾,而后对无噪声理想情况下感知矩阵需要满足的NSP准则、实际应用中含噪声情况下感知矩阵需要满足的RIP准则作了详细的论述,并对RIP准则对于感知矩阵的必要性作了适当地证明。
In compressed sensing theory (CS), whether the sensing matrix meets the RIP criterion directly determines the quality of the reconstructed signal. In practice, if the perceptual matrix does not meet the RIP guidelines, the reconstructed signal can not be used at all because of large errors. Therefore, the perceptual matrix satisfies the finite isometry criterion (RIP) is one of the few basic principles in CS. In this paper, the compressed sensing theory is briefly reviewed. Then, the NSP criterion that the perceptual matrix needs to meet in the case of no noise and the RIP criterion that the perceptual matrix needs in the practical application are discussed in detail, and the RIP The guidelines properly justify the need for a perception matrix.