Wavelet Packets and Their Statistical Applications

Description

This book presents the basic concepts of functional analysis, wavelet analysis and thresholding. It begins with an elementary chapter on preliminaries such as basic concepts of functional analysis, a brief tour of the wavelet transform, Haar scaling functions and function space, wavelets, symlets wavelets and coiflets wavelets. In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds. Chapter 4 discusses characterisations of function spaces like Lebesgue spaces, Hardy spaces and Sobolev spaces in terms of wavelet packets, while Chapter 5 is devoted to applications of wavelets and wavelet packets in speech denoising and biomedical signals. In closing, Chapter 6 highlights applications of wavelets and wavelet packets in image denoising. Front Matter ....Pages i-xvii Preliminaries (Khalil Ahmad, Abdullah)....Pages 1-36 Wavelet Packets (Khalil Ahmad, Abdullah)....Pages 37-77 Convergence of Wavelet Packet Series (Khalil Ahmad, Abdullah)....Pages 79-91 Function Spaces and Wavelet Packets (Khalil Ahmad, Abdullah)....Pages 93-129 Applications in Signal Processing (Khalil Ahmad, Abdullah)....Pages 131-201 Applications in Image Processing (Khalil Ahmad, Abdullah)....Pages 203-224 Back Matter ....Pages 225-238