The chaotic dynamics of high-dimensional systems

This paper introduced a new method to exploit chaotic, sparse representations of nonlinear time series data. The methodology of the algorithm included two steps. First, the proposed method applied the fractal theory to estimate optimal dimension in a compressive sensing of a time series, and sparse data were concentrated on a pseudo-orbit trajectory. Second, the chaotic trajectory was extracted from the data obtained from the first step by employing a chaos prediction method. To verify the efficiency of the proposed method, the algorithm is applied to three categories, consisting of chaotic noise reduction, signal compression, and image compression. The experimental results indicated that the proposed method outperformed other state-of-the-art methods with up to a 95% reduction in errors. Moreover, the results demonstrated that sparse, chaotic representation was most effective in signal and image compression.