Wavelet Ten Lectures

Author: Ingrid Daubechies (USA)
Translator: Li Jianping
Publisher:
Publish Date: 2004-05-01
Features: The original book "Ten Lectures on Wavelets" was awarded the Leroy P. Steele Prize in 1994 for its outstanding contributions and elegant style. The book has a print run exceeding 15,000 copies and has become widely popular worldwide, which is extremely rare for academic works. "The author, Daubechies, is one of the main founders of wavelet analysis theory, and the book describes the main principles and methods of wavelet analysis in concise language, making it an excellent textbook for wavelet courses. The book is highly engaging to read, like reading an excellent Russian novel. Daubechies skillfully organizes the material, provides explanations and annotations in many places, and effectively resolves difficulties. This book meets the needs of personal reading as well as university students, graduate students, university teachers, and researchers, and will become a classic." F. Alberto Gr?nbaum, Science, August 7, 1992.
"This book is both an introductory textbook on wavelet analysis and an academic monograph that comprehensively summarizes and reflects the latest research results in the field. The book includes numerous practical examples and describes many applications of wavelet analysis, such as signal processing, image coding, and numerical analysis." Albert Cohen, Mathematical Reviews, Issue 93e.
"This is an excellent book written by one of the main founders of wavelet theory, and its content is an important part of the physical principles, mathematical methods, and engineering analysis of wavelet analysis. The book is written with sharp wit, rigorous reasoning, and a gradual progression from simple to complex, with broad applications. It holds significant reference value for mathematicians, physicists, engineering technicians, and anyone interested in wavelet analysis applications." Nicolae Popa, Romanian Journal of Pure and Applied Mathematics, Vol. 16, Nos. 1-2, 1996.
Ingrid Daubechies is a professor in the Department of Mathematics at Princeton University and the Center for Applied and Computational Mathematics. She worked in the Department of Theoretical Physics at the Free University of Brussels before joining the Bell Labs of AT&T as a senior researcher. She is also a professor at the Department of Mathematics at the University of Louvain. She received the Ruth Lyttle Satter Mathematics Award in 1997. She has been frequently invited to give academic lectures worldwide and has published a large number of academic papers and books.
The original book "Ten Lectures on Wavelets" is a classic academic masterpiece recognized worldwide and an outstanding book with a significant impact in modern mathematics. It includes the most advanced achievements in wavelet analysis worldwide since the 1980s, as well as Daubechies' own remarkable contributions to compactly supported wavelets. For those studying and researching wavelet theory and exploring the applications of wavelet analysis, this book is an essential classic. The academic value and ideas of the book have been highly praised by the prominent French mathematician Y. Meyer, one of the main founders of wavelet analysis theory, and it has made significant contributions to the popularization and promotion of wavelet analysis worldwide. Researchers in universities, research institutions, and renowned R&D departments of famous enterprises in foreign and overseas countries have long regarded this book as an important reference and an introductory text for learning wavelet analysis.
The original author, Ingrid Daubechies, is one of the main founders of wavelet analysis. She established the Daubechies wavelet basis, which is the first wavelet basis with good application effects in the world. The Daubechies wavelet basis is the most widely used wavelet basis function internationally and is a key part of the JPEN 2000 international standard, making wavelet analysis a true applied discipline and a focal point of international research.
Chapter 1 of this book provides a general description of wavelet transforms, while the subsequent chapters offer more detailed explanations. Chapter 2 introduces the continuous wavelet transform, Chapter 3 introduces the discrete wavelet transform and frames, and Chapter 4 introduces time-frequency density and orthogonal bases. In these chapters, many conclusions about windowed Fourier transforms and wavelet transforms are demonstrated, and the two are parallel, making it convenient for readers to compare and distinguish them. Chapter 5 introduces orthogonal wavelet bases and multiresolution analysis, and Chapter 6 introduces...