Polynomial Phase Signal Denoising via Sparse Representations Over a SMAF-Based Dictionary Learning Algorithm

In this paper, we address the problem of denoising polynomial phase signals (PPS) by removing additive white Gaussian noise. Our approach is based on sparse representation using a trained dictionary, which is obtained through the secondary moving average filtering (SMAF) dictionary learning algorithm. The proposed algorithm consists of two main steps: first, we utilize K-SVD or other dictionary learning algorithms to obtain the initial trained dictionary; second, we apply the SMAF method to modify the dictionary atoms, enabling them to behave more smoothly and effectively reducing the noise present in the atomic structures. Consequently, the signal-to-noise ratio (SNR) of the reconstructed signal using sparse representation over the refined dictionary is significantly improved compared to K-SVD and RLS-DLA. To achieve optimal denoising effectiveness, we first estimate the SNR of the PPS using our proposed SNR estimation algorithm. Based on the estimated SNR, we then determine the number of samples for the moving average filter impulse response.