基于非相干准则的压缩感知观测矩阵设计的极大极小方法

针对固定的正交基,利用观测矩阵与稀疏基的非相干准则,研究确定性观测矩阵的设计问题。观测矩阵与稀疏基的相干性越小,压缩采样所需的观测个数就越少,包含原始信号的信息就越多,重构概率越高。根据观测矩阵与稀疏基的相干性定义,对固定的已知正交基,构建满足最优非相干性的极大极小问题,寻找与正交基最不相干的观测矩阵。最后,以固定正交基为离散余弦基的情形为算例,与常用观测矩阵对应的相干性做比较,验证了本文方法的有效性。

The Minimax Method of Design of Measurement Matrices for Compressed Sensing Based on Incoherence Criterion

For the fixed orthonormal basis, the design of the determinate measurement matrix is investigated by using the incoherence criterion between the measurement matrix and the sparse basis. The smaller the coherence between the measurement matrix and the sparse basis is, the less the required measurement number in the process of compressed sampling is, the more information in the original signal will be contained, and the higher the probability of restructure is. According to the definition of coherence between the measurement matrix and the sparse basis, the minimax method of satisfying optimal incoherence is constructed for the fixed known orthonormal basis, furthermore, the measurement matrix that is most incoherent with the orthonormal basis can be found. Finally, to verify the effectiveness of the method mentioned in this paper, the comparison, between a numerical simulation example of taking the fixed orthonormal basis as a discrete cosine basis and the coherence corresponding to the common measurement matrices, is made.