A Chaotic Signal Denoising Method Based on Feature Mode Decomposition and Amplitude-Aware Permutation Entropy

Chaotic signals commonly exhibit nonlinear and nonstationary characteristics, while noise contamination reduces signal interpretability and degrades subsequent feature extraction and dynamical analysis. To improve the stability of mode-boundary determination and mitigate reconstruction distortion, this paper proposes a hybrid denoising framework that integrates feature mode decomposition (FMD), amplitude-aware permutation entropy (AAPE), dual-tree complex wavelet transform (DTCWT), and Savitzky–Golay (SG) filtering. First, the noisy signal is decomposed into multiple mode components using FMD. Then, the AAPE of each mode is calculated to adaptively distinguish high-frequency noise-dominant modes from non-high-frequency modes. For the high-frequency noise-dominant modes, improved logarithmic threshold shrinkage is applied to the magnitudes of DTCWT complex coefficients to suppress random noise and reduce threshold-induced bias. For the non-high-frequency modes, SG filtering is employed to further attenuate residual noise while preserving local waveform structures. Finally, the processed modes are reconstructed to obtain the denoised signal. Experiments on a simulated Lorenz chaotic signal and a real-world sunspot time series demonstrate that, across different noise levels, AAPE provides more stable mode partitioning than ApEn, CC, and CMSE. Moreover, under Gaussian white noise, Poisson noise, and uniform noise, the proposed method generally achieves a higher output signal-to-noise ratio (SNR) and a lower root mean square error (RMSE) than WT, CEEMD, EEMD, CEEMDAN+LMS, and VMD, while also yielding better performance in phase-space reconstruction and temporal-detail recovery. These results verify the effectiveness and practical applicability of the proposed method for chaotic signal denoising.