Local Projection Denoising for Chaotic Signals

In my research, I implemented a local projection denoising method specifically designed for chaotic signal processing. The algorithm operates by projecting noisy signal trajectories onto local tangent spaces of the underlying attractor, effectively separating noise components from deterministic chaotic structures. The implementation involved coding the following key components: nearest neighbor identification for phase space reconstruction, local covariance matrix computation, and eigenvalue decomposition for noise subspace separation. Through systematic debugging and validation tests, the code successfully demonstrates robust denoising performance while preserving essential chaotic characteristics. A significant advantage of this approach lies in its ability to retain meaningful dynamical information while filtering out noise contamination, thereby enhancing signal quality for subsequent analysis like Lyapunov exponent calculation or attractor dimension estimation. The algorithm particularly excels in handling chaotic signals where traditional linear filtering methods would distort nonlinear characteristics. I hope this research provides valuable insights for fellow researchers working with nonlinear signal processing, and that my code implementation serves as a practical reference for developing similar denoising applications in chaos analysis and time series processing.