Multiscale Modeling Beyond Wavelets

The book is an introduction to the methods that deal with problems raised in using multiscale mathematical/statistical models such as wavelets and other multiscale systems. Special emphasis is given to the applications in filter design, sampling and nonparametric statistical methods for signal modeling, detection and recovering as well as learning and prediction. Applications of these methods notably to signal distortion treatment (Gibbs phenomenon), misisng sample identification, pattern recognition and maching learning problems are discussed and illustrated by examples. Both continuous and sampled (digitized) signals are considered. These methods are in contrast to more traditional methods involving mainly Fourier series withwhich they will also be compared. These multiscale methods have better localization properties, but also avoid excessive oscillations often encountered inboth signal and image analysis.