一种三阶多项式相位信号去噪的字典学习算法

在加性高斯白噪声的影响下，对于三阶多项式相位信号(CPS)，经典的字典学习算法，如K-means Singular Value Decomposition(K-SVD)， 递归最小二乘字典学习算法(RLS-DLA)和K-means Singular Value Decomposition Denoising (K-SVDD)得到的学习字典，通过稀疏分解，不能有效去除信号的噪声。为此，该文提出了针对CPS去噪的字典学习算法。该算法首先利用RLS-DLA对的字典进行学习；其次采用非线性最小二乘(NLLS)法修改了该算法对字典更新的部分；最后对训练后的字典通过对信号的稀疏表示得到重构信号。对比其它的字典学习算法，该算法的信噪比(SNR)值明显高于其它算法，而均方误差(MSE)显著低于其它算法，具有明显的降噪效果。实验结果表明，采用该算法得到的字典通过稀疏分解，信号的平均信噪比比K-SVD, RLS-DLS和K-SVDD高出9.55 dB, 13.94 dB和9.76 dB。

A Dictionary Learning Algorithm for Denoising Cubic Phase Signal

Under the influence of additive white Gaussian noise, the classical dectionary learning algorithms, such as K-means Singular Value Decomposition (K-SVD), Recursive Least Squares Dictionary Learning Algorithm (RLS-DLA) and K-means Singular Value Decomposition Denoising (K-SVDD), can not effectively remove the noise of Cubic Phase Signal (CPS). A novel dictionary learning algorithm for denoising CPS is proposed. Firstly,the dictionary is learned by using the RLS-DLA algorithm. Secondly,the update stage of the RLS-DLA algorithm is modified by using Non-Linear Least Squares (NLLS) in the algorithm. Finally, the signal is reconstructed via sparse representations over learned dictionary.Signal to Noise Ratio (SNR) obtained by using the novel dictionary learning algorithm is obviously higher than other algorithms,and the Mean Squares Error (MSE)  obtained by using the novel dictionary learning algorithm is obviously lower than other algorithms. Therefore there is obviously denoising performance for using the dictionary learned by the algorithm to sparsely represent CPS. The experimental results show that the average SNR obtained by using the algorithm is 9.55 dB, 13.94 dB and 9.76 dB higher than K-SVD, RLS-DLS and K-SVDD.