A study on data compression by dynamical system approach

Abstract

The importance and demands for data compression have been increasing rapidly, especially with the growing popularity of Internet access and multimedia personal entertainment. The ratio and the quality of compression data are main concern when judging the compression algorithm. Recently, data compression techniques are dominated by the fast Fourier and wavelet transforms, which approximate the given sequence as a linear sum of the basis function, by retaining a finite number of coefficients to achieve the goal of compression. In this project, we introduce a dynamical system approach, which compresses data in a totally different way from the ones mentioned above. Taking advantage of the fact that Leaky-integrator model recurrent neural net can approximate arbitrary finite sequence, we demonstrate in this thesis how to compress UV and IR spectrum by a discrete-time recurrent neural net. As this is an initial valued problem, the information we need to store is the parameters of the system and the initial states. Compression ratio is also discussed in this thesis.