Enhancing Adaptive Capability of Wavelet Analysis Methods for Chaotic Signal Denoising

Wavelet analysis faces challenges in adaptive capability when applied to chaotic signal denoising. Traditional fixed-threshold methods struggle to handle the nonlinear and multi-scale characteristics of chaotic signals. To address this issue, we introduce adjustment factors and optimization strategies to enhance method adaptability.

The core approach combines correlation dimension characteristics of chaotic sequences to determine optimal thresholds at different scales. As an important feature of chaotic signals, correlation dimension reflects signal complexity and noise level, making it suitable for threshold selection criteria. For efficient optimal threshold search, we employ genetic algorithms for global adaptive optimization. Genetic algorithms simulate natural selection processes, enabling rapid identification of superior solutions in complex parameter spaces while avoiding local optima.

When applied to Lorenz chaotic time series denoising experiments, results demonstrate that the adaptive strategy significantly improves denoising performance. By dynamically adjusting thresholds across different scales, the method effectively suppresses noise while preserving critical features of chaotic signals. This approach provides new insights for addressing denoising problems in complex nonlinear signal processing.