利用有限域上的多项式图构造感知测量矩阵的研究

Measurement Matrix Constructionvia Polynomial Graphs in the Finite Field for Compressed Sensing

测量矩阵的构造是压缩感知(Compressed Sensing,CS)的重要内容之一。目前关于测量矩阵构造主要有随机性和确定性生成两种方式。尽管确定性的测量矩阵重构信号的精度一般不如随机矩阵,但确定性的测量矩阵易于硬件实现。给出了有限域上多项式图的相关概念,并利用有限域上多项式图作为工具,深入地研究讨论了一个满足限制等距性质(RIP)的感知测量矩阵确定性构造方法。

The measurement matrixconstruction is one of the important contents in Compressed Sensing （CS）. At present, the measurement matrix construction mainly includes randomness and determinism methods. Although the accuracy of reconstructing signal by the random matrixis generally better, the de- terministic measurement matrix is much easier to implement in hardware. This paper gives the concept of polynomial graphs on finite fields, and uses it as a tool to study and discuss a deterministic construc- tion on the measurement matrices satisfying the restricte disometry property （RIP）.