Wavelet Packets and Their Statistical Applications

✍ Scribed by Khalil Ahmad, Abdullah

• Publisher: Springer Singapore
• Year: 2018
• Tongue: English
• Leaves: 249
• Series: Forum for Interdisciplinary Mathematics
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Mathematics; Functional Analysis; Numerical Analysis; Applications of Mathematics; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Signal, Image and Speech Processing