基于选择性测量的压缩感知去噪重构算法

Denoising recovery for compressive sensing based on selective measure

针对压缩感知中噪声折叠现象严重影响稀疏信号重构性能的问题,提出一种基于选择性测量的压缩感知去噪重构算法。首先从理论上解释了压缩感知中噪声折叠现象;然后提出一种基于测量数据的特征统计量,推导分析其概率密度函数,并基于此构造一种噪声滤波矩阵,用于优化测量矩阵,实现智能地选择信号分量、过滤噪声分量,提高测量数据信噪比;最后,通过增加测量数据获取次数可进一步提升算法重构性能。仿真实验表明,基于选择性测量的压缩感知去噪重构算法明显改善了低信噪比条件下信号的重构性能。

In order to reduce the effect of noise folding（NF） phenomenon on the performance of sparse signal reconstruction,a new denoising recovery algorithm based on selective measure was proposed.Firstly,the NF phenomenon in compressive sensing（CS） was explained in theory.Secondly,a new statistic based on compressive measurement data was proposed,and its probability density function（PDF） was deduced and analyzed.Then a noise filter matrix was constructed based on the PDF to guide the optimization of measurement matrix.The optimized measurement matrix can selectively sense the sparse signal and suppress the noise to improve the SNR of the measurement data,resulting in the improvement of sparse reconstruction performance.Finally,it was pointed out that increasing the measurement times can further enhance the performance of denoising reconstruction.Simulation results show that the proposed denoising reconstruction algorithm has a better improvement in the performance of reconstruction of noisy signal,especially under low SNR.