Stochastic processes: multiscale processing and applications to signal and image compression

  • Albert Cohen
  • Robert D. Ryan
Part of the Applied Mathematics and Mathematical Computation book series (AMMC)


Multiscale decompositions are non-parametric in the sense that they do not require any specific assumptions about the data to be decomposed. We require only that these data lie in a reasonable function or sequence space. So far, we have studied the different aspects of multiresolution approximation and wavelets without considering the properties of the functions or signals that one wishes to process in practical applications. We now want to check the effect of these properties on the resulting multiscale decompositions. Specifically, we wish to address the following kinds of questions:
  • How well can a signal of a certain type be approximated in the spaces V j ? This is typically a linear approximation process, since this approximation can be performed by the projection operator.

  • How well can a signal of a certain type be approximated by a combination of N wavelets? This, in contrast, is a non-linear approximation process, because we allow the choice of these wavelets to depend on the signal.

  • Are these approximations better than those that are obtained if we replace the wavelet basis by the trigonometric system?


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Albert Cohen
    • 1
  • Robert D. Ryan
    • 2
  1. 1.University of Paris VIFrance
  2. 2.ParisFrance

Personalised recommendations