一种基于数据平滑的压缩感知信号重构法

A reconstruction algorithm applicable to compressive sensing by data smoothing

本文针对压缩感知中低信噪比信号重构问题,提出了一种基于数据平滑的信号重构算法。算法分为两步,第一步将采样值分段,并求出连续若干段采样矢量的算术平均值;第二步针对采样矢量的算术平均值,基于l1-范数最小准则估计其非零系数位置用于构造信号子空间,而后利用获得的信号子空间针对每段采样矢量分别求解非零系数的值,并重构信号。该方法适用于稳定信号,理论分析与仿真都表明本算法的性能优于标准正交匹配追踪方法。

In this paper,a reconstruction algorithm applicable to compressed sensing by data smoothing for stable low SNR signal is proposed.The algorithm is divided into two steps： the first step is to intercept the samples and then get the arithmetic mean of several continuous sections of sample vectors.The second step is to locate the position of the non-zero coefficients according to the mean sample vector based on l1-norm minimization so as to construct the signal subspace.Then,solve the value of the non-zero coefficients according to each sample vector based on l2-norm minimization and reconstruct the signal.This method is suitable for the reconstruction of stable signal.Both the analysis and the simulation show that in the noisy setting,the performance exceeds that of the standard orthogonal matching pursuit algorithm.