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Two-Dimensional Wavelets and their Relatives
2004
https://doi.org/10.1017/CBO9780511543395visibility
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16 pages
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Abstract
Two-Dimensional Wavelets and their Relatives Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms when processing rapidly varying functions and signals. In particular, they offer benefits for real-time applications such as medical imaging, fluid dynamics, shape recognition, image enhancement and target tracking. This book introduces the reader to 2-D wavelets via 1-D continuous wavelet transforms, and includes a long list of useful applications. The authors then describe in detail the underlying mathematics before moving on to more advanced topics such as matrix geometry of wavelet analysis, three-dimensional wavelets and wavelets on a sphere. Throughout the book, practical applications and illustrative examples are used extensively, ensuring the book's value to engineers, physicists and mathematicians alike.
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We live in the Information Age where information is analyzed, synthetized, and stored at a much faster rate using different techniques such as different wavelets and wavelet transforms. For many decades, wavelets and wavelet transforms have received much attention in the literature of many communities in the areas of science and engineering. There are different types of wavelets. These wavelets are used as analyzing tools by pure mathematicians (in harmonic analysis, for the study of vii Calderon-Zygmund operators), by statisticians (in nonparametric estimation), and by electrical engineers (in signal analysis). In physics, wavelets are used because of their applications to time-frequency or phase-space analysis and their renormalization concepts. In computer vision research, wavelets are used for "scale-space" methods. In stochastic processes, they are used in application of self-similar processes. 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Topics such as decomposition and reconstruction algorithms, subdivision algorithms, fast numerical computations, frames, time-frequency localizations, and continuous-and discrete-wavelet transforms are covered for their use of wavelets and wavelet transforms. In addition, topics such as fractals and fractal transforms, mixed signal systems, sub-band coding, image compression, real-time filtering, radar applications, transient analysis, medical imaging, segmentation, blockchain systems, information security, and vibration in aeroelastic systems are some of the areas covered in the book. Applications of many of these wavelets and wavelet transform analyses are developed across disciplines in the book. This book, entitled Wavelets and Wavelet Transform Analysis and Applications: A Signal Processing Approach is a unique book because of its in-depth treatment of the applications of wavelets and wavelet transforms in many areas across many disciplines. The book does this in a very simplified and understandable manner without the mathematical rigor that scares many people away from the field. It uses lots of diagrams to illustrate points being discussed. In addition, the concepts introduced in the book are reinforced with review questions and problems. MATLAB codes and algorithms viii Preface Preface ix x Preface I thank Prairie View A&M University (PVAMU) and The Texas A&M University Board of Regents that approved the Center of Excellence for Communication Systems Technology Research (CECSTR) as one of the Board of Regents Approved Centers on the Campus of PVAMU and within the entire Texas A&M System. I thank all the student researchers and faculty colleagues at CECSTR and the College of Engineering, especially my colleagues in the Department of Electrical and Computer Engineering for all their support. My special thanks go to our former president, Dr. George Wright; former provost, Dr. Thomas-Smith; and former vice president for research and a great friend Dr. Willie Trotty. Special thanks to my former dean of the College of Engineering, Dean Bryant, for all his support. Without the help and support of these giants, there would not be CECSTR, and therefore there would not have been the kind of research work that may have resulted in some of the information in this book. Finally, I thank my wife Caroline Chioma Akujuobi and my two sons Obinna and Chijioke Akujuobi for their patience, encouragement, and support throughout the time I was preparing the manuscript for this book.
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