An Adaptive Denoising Algorithm for Noisy Chaotic Signals Based on Local Sparse Representation

An adaptive denoising algorithm based on local sparse representation (local SR) is proposed. The basic idea is applying SR locally to clusters of signals embedded in a high-dimensional space of delayed coordinates. The clusters of signals are represented by the sparse linear combinations of atoms depending on the nature of the signal. The algorithm is applied to noisy chaotic signals denoising for testing its performance. In comparison with recently reported leading alternative denoising algorithms such as kernel principle component analysis (Kernel PCA), local independent component analysis (local ICA), local PCA, and wavelet shrinkage (WS), the proposed algorithm is more efficient.