基于卡尔曼滤波的压缩感知弱匹配去噪重构

发布时间：2018-08-19 19:50

【摘要】：现有的贪婪迭代类压缩感知重构算法均基于最小二乘对信号进行波形估计,未考虑到可能将量测噪声引入信号估计的情况.针对以上不足,提出了一种基于线性Kalman滤波的压缩感知弱匹配去噪重构算法.该算法不需已知稀疏度先验,通过引入Kalman滤波,在最小均方误差准则下,每次迭代都获得最佳信号估计;并以弱匹配的方式同时筛选出有效的原子,并剔除冗余原子进而重构原信号.新算法继承了现有贪婪迭代类算法的有效性,同时避免了因噪声干扰或稀疏度未知导致的重构失败.理论分析和实验表明,新算法在同等条件下,重构性能优于现有典型贪婪迭代类算法,且其运算时间低于BPDN算法和同类的KFCS算法.
[Abstract]:The existing greedy iterative class compression perceptual reconstruction algorithms are based on the least squares to estimate the signal waveform without considering the possibility of the measurement noise being introduced into the signal estimation. In order to solve the above problems, a new algorithm of compression perception weak matching denoising and reconstruction based on linear Kalman filter is proposed. This algorithm does not need to know a priori degree of sparsity. By introducing Kalman filter, the optimal signal estimation is obtained in every iteration under the minimum mean square error criterion, and the effective atoms are screened simultaneously in a weakly matched manner. The redundant atoms are removed and the original signal is reconstructed. The new algorithm inherits the validity of the existing greedy iterative algorithms and avoids the reconstruction failure caused by noise interference or unknown sparsity. Theoretical analysis and experiments show that the reconstruction performance of the new algorithm is better than that of the classical greedy iterative algorithms under the same conditions, and the computation time of the new algorithm is lower than that of the BPDN algorithm and the similar KFCS algorithm.
【作者单位】：海军航空工程学院信号与信息处理山东省重点实验室;
【基金】：“泰山学者”建设工程专项经费资助海军航空工程学院研究生创新基金资助
【分类号】：TN911.4

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