Wavelet packets and their statistical applications

✍ Scribed by Ahmad K.

• Publisher: Springer
• Year: 2018
• Tongue: English
• Leaves: 249
• Series: Forum for interdisciplinary mathematics
• 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.  Read more...

Abstract: 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

Content: Chapter 1. Preliminaries --
Chapter 2. Wavelet Packets --
Chapter 3. Convergence of Wavelet Packet Series --
Chapter 4. Function Spaces and Wavelet Packets --
Chapter 5. Applications in Signal Processing --
Chapter 6. Applications in Image Processing.

✦ Subjects

Functional analysis.;Applied mathematics.;Engineering mathematics.;Numerical analysis.;Statistics.;Mathematics.;Functional Analysis.;Numerical Analysis.;Applications of Mathematics.;Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.;Signal, Image and Speech Processing.;Wavelets (Mathematics)