The chaotic dynamics of high-dimensional systems

This paper introduced a new method toexploit chaotic, sparse representations of nonlineartime series data. The methodology of the algorithmincluded two steps. First, the proposed method appliedthe fractal theory to estimate optimal dimension in acompressive sensing of a time series, and sparse datawere concentrated on a pseudo-orbit trajectory. Second,the chaotic trajectory was extracted from the dataobtained from the first step by employing a chaos predictionmethod. To verify the efficiency of the proposedmethod, the algorithm is applied to three categories,consisting of chaotic noise reduction, signal compression,and image compression. The experimental resultsindicated that the proposed method outperformed otherstate-of-the-art methods with up to a 95% reduction inerrors. Moreover, the results demonstrated that sparse,chaotic representation was most effective in signal andimage compression.