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.
Covers new material such as chromatic derivatives for signal processing and presents a more modern account of prolate spheroidal functionsCovers the positive filter and filter bank design using orthogonaland biorthogonal waveletsDiscusses multi-parameter filters using Slepian functions and wavelets and FIR using periodic Slepian functions and waveletsProvides extensive numerical techniques needed to achieve actual implementations using MAATLAB programs