A secondary EWMA-based dictionary learning algorithm for polynomial phase signal denoising

Under the influence of additive white Gaussian noise, sparse representation cannot effectively remove noise associated with the polynomial phase signal (PPS) via most dictionary learning algorithms whose training data come from the noisy signal, such as K-SVD and RLS-DLA. In this paper, we present a novel dictionary learning algorithm based on secondary exponentially weighted moving average (SEWMA) to denoise PPS. In the proposed algorithm, we first estimate the signal-to-noise (SNR) of the PPS to set the optimal rate of a weighted decline using covariance matrix model. Second we use RLS-DLA to train the dictionary. Thirdly, SEWMA is used to refine atoms in the learned dictionary. In this way, the SNR of the reconstructed signal obtained using the proposed algorithm is clearly higher than that of other algorithms, whereas the mean squared error is lower than that of other algorithms. To obtain the optimal denoising performance, the optimal rate of a weighted decline is set based on the estimated SNR. Simulation results show that the proposed method outperforms the K-SVD, RLS-DLA in mean square error and the SNR.