基于DCFT的Chirp矩阵采样重构算法

Reconstruction Algorithm of Chirp Matrix Sampling Based on DCFT

在Chirp矩阵的压缩采样中,针对离散傅里叶变换(DFT)相关检测算法重构精度较差、可用信号稀疏度有限的问题,提出一种基于离散Chirp-Fourier变换(DCFT)的重构算法。根据信号稀疏度k增加采样数,使采样矩阵具有对k值大的信号有准确重构的能力;选择采样信号k个最大的DCFT幅值所对应的原子索引来击中信号非零元的位置,以减少DFT相关算法中交调干扰造成的最佳原子误检测;利用最小二乘法估计各非零元的幅值,进一步减小重构误差。对长度为1 681的一维信号进行采样和重构实验,结果表明,该算法重构的信号稀疏度增大至DFT相关检测算法的4倍,并且时间复杂度仍为O(kN)。

Aiming at the problem of the poor reconstruction accuracy and the limited sparsity of the signal available of the DFT correlation detection algorithm in the compressed sampling using chirp matrix,this paper proposes a Discrete Chirp-Fourier Transform（DCFT） based reconstruction algorithm.It increases the number of measurements according to the signal sparsity k so that the sampling matrix has the ability of reconstructing accurately the signal having a large value of k.And it selects the atom indexes corresponding to the k largest DCFT amplitude of the sampling signal to hit the nonzero positions to reduce the incorrect detection of the best atoms caused by cross interference in the DFT correlation algorithm.It uses the Least Square method to estimate the amplitudes of nonzero elements to further reduce the reconstruction error.Results of sampling and reconstruction experiments of onedimensional signal with length N of 1 681 show that the DCFT reconstruction algorithm can reconstruct accurately the signal whose sparsity k increases to 4 times as that of the DFT correlation detection algorithm,and has a considerable computational complexity O （kN）.