Chaotic Signal Denoising Algorithm Based on Self-Similarity

Inspired by the self-similar fractal properties of chaotic attractors and the heuristics of similarity filtering of images, a novel chaotic signal denoising algorithm is proposed. By grouping the chaotic signal with similar segments, the denoising of one-dimensional input is transformed into a two-dimensional joint filtering problem. Singular value decomposition is performed on the grouped signal segments and the transform coefficients are processed by thresholding to attenuate noise and finally undergo inverse transformation to recover the signal. Because the similar segments in the grouping have good correlation, the two-dimensional transformation of the grouping can obtain a more sparse representation of the original signal compared with the threshold value denoising in the direct one-dimensional transform domain, thereby having better noise suppression effect. Simulation results show that the algorithm can improve the reconstruction accuracy and has better signal-to-noise ratio than existing chaotic signal denoising algorithms.