Nonlinear Dynamics

, Volume 52, Issue 1–2, pp 51–70 | Cite as

Generating an adaptive multiresolution image analysis with compact cupolets

  • Kourosh Zarringhalam
  • Kevin M. Short
Original Paper


We present an efficient control scheme for stabilizing unstable periodic orbits of chaotic systems. The resulting orbits are called cupolets and have been proven to be useful in the representation of oscillatory or quasi periodic signals such as appear in music and image compression (Short et al., AES 118th Convention preprint 6446, May 2005; Short et al., AES 119th Convention preprint 6588, October 2005). In this paper we show that these cupolets can be used effectively to produce an adaptive basis for the space of real-valued functions of a discrete variable. From this basis, we construct a multiresolution analysis which allows for the approximation of signals at different resolution levels and apply it to image compression. This adaptive multiresolution analysis provides an interesting continuum between Fourier analysis and wavelet analysis.


Controlling chaos Cupolets Image compression Signal processing Unstable periodic orbits 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of New HampshireDurhamUSA

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