一种基于PEG的构造矩阵在压缩感知中的应用

Application of a PEG-based Construction Matrix in Compressed Sensing

压缩感知(Compressed Sensing,CS)中测量矩阵是获取原始信号数据结构和信息的关键,测量矩阵的研究为压缩感知理论在具体场景中的应用提供理论基础。通过比较稀疏空间中的信号重构问题与线性解码问题,论述了压缩感知理论与低密度奇偶校验码(Low-density Parity-check,LDPC)间的理论联系,得出结论:稀疏校验矩阵可以作为压缩感知测量矩阵。为验证结论,提出了分组渐进边生长算法(Progressive-edge-growth by Group,G-PEG),该算法改善了矩阵生成速度并在分组中保留了随机特性。仿真结果表明,G-PEG矩阵是一种性能优良的测量矩阵。

The measurement matrix in Compressed Sensing is the key to obtain the original signal data structure and information.The research of measurement matrix provides theoretical basis for the application of compressed sensing theory in specific scenarios.By comparing the signal reconstruction problem and linear decoding problem in sparse space,the article discusses the theoretical relationship between compressed sensing theory and low-density parity-check(LDPC),and concludes:sparse check matrix can be used as a compressed sensing measurement matrix.In order to verify the conclusion,a Progressive-edge-growth by Group(G-PEG)algorithm is proposed,which improves the speed of matrix generation and retains random characteristics in the group.Simulation results show that the G-PEG matrix is a measurement matrix with excellent performance.