A measurement matrix and sensing dictionary are the basic tools for signal compression sampling and reconstruction, respectively, which are important aspects in the field of compression sensing. Previous studies which have divided the measurement matrix and sensing dictionary into two separate processes did not make full use of their inherent intercorrelations. In case of which could be fully utilized, the mutual coherence of the atoms of measurement matrix and sensing dictionary can be further reduced under the premise of ensuring that the original signal information is stored, which could improve the accuracy of signal recovery. The present study attempted to reduce the mutual coherence between the sensing dictionary and measurement matrix by proposing the t-average mutual coherence coefficient as an evaluation index for the sensing dictionary. A mathematical model for co-constructing a measurement matrix and sensing dictionary is firstly proposed. Then, the measurement matrix and sensing dictionary cooperative construction(MSCA)algorithm is proposed to solve the model at a faster rate. The simulated results for sparse signal and binary image show that the proposed algorithm has faster computing speed and higher solution precision than the state-of-the-art construction algorithms.

测量矩阵和传感字典分别是信号压缩采样和重建的基本工具，这是压缩传感领域的重要方面。先前将测量矩阵和传感字典分为两个独立过程的研究并未充分利用其固有的相互关系。在可以充分利用的情况下，在保证存储原始信号信息的前提下，可以进一步降低测量矩阵原子与传感词典的原子之间的相干性，可以提高信号恢复的准确性。本研究试图通过提出t平均互相关系数作为感测字典的评估指标，来减少感测字典和测量矩阵之间的互相关性。首先提出了一种用于共同构建测量矩阵和感知字典的数学模型。然后，提出了测量矩阵和感知字典协同构造算法，以更快的速度求解模型。对稀疏信号和二进制图像的仿真结果表明，与最新的构造算法相比，该算法具有更快的计算速度和更高的求解精度。