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压缩感知是针对稀疏信号和可压缩信号,在信号采样的同时对数据进行压缩。其中,测量矩阵对信号采集和重建算法有着重要的影响。随机矩阵虽然有较好的重建效果,但硬件实现较为复杂。相反,确定性测量矩阵有硬件实现的优势。本文依据一维信号与二维图像特性,采用广义轮换矩阵作为确定性测量矩阵,对信号采取非均匀采样,通过调整测量矩阵系数强化低频段采样,同时增强测量矩阵列向量非相关性。实验结果表明,广义轮换矩阵的性能不仅优于同类确定性测量矩阵,而且优于高斯矩阵等随机测量矩阵。
Compressed sensing is for sparse signals and compressible signals, which compress the data as it is sampled. Among them, the measurement matrix has an important influence on signal acquisition and reconstruction algorithms. Although the random matrix has a good reconstruction effect, but the hardware is more complicated. In contrast, deterministic measurement matrices have the hardware implementation advantages. In this paper, based on the characteristics of one-dimensional signal and two-dimensional image, the generalized rotation matrix is used as a deterministic measurement matrix, the signal is non-uniformly sampled, the low frequency band samples are enhanced by adjusting the measurement matrix coefficients, and the non-correlation of column vectors is enhanced. The experimental results show that the performance of generalized rotation matrix is not only better than the same deterministic measurement matrix, but also better than the random measurement matrix such as Gaussian matrix.