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Author(s): | Wolfgang Härdle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
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Publisher: | Springer
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Year: | 2000
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English |
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Pages: |
254 pages |
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Size: | 1.54 MB
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Extension: | PDF |
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[content title="Summary"] **Title: Wavelets: Theory and Applications**
**From the Publisher:**
The mathematical theory of wavelets, developed by Yves Meyer and many collaborators over the past decade, has emerged as a powerful tool for approximating irregular functions and surfaces. Initially applied to fields such as data compression, turbulence analysis, and image and signal processing, wavelet theory has expanded its scope and found widespread use in a variety of areas, particularly in nonparametric statistical analysis.
As wavelet theory continued to evolve, it became clear that it offered a flexible and effective framework for addressing complex, real-world problems, especially in fields where traditional methods struggled. The theory has also seen a surge of interest in the development of efficient computational methods, leading to widespread adoption in the 1990s. This book serves as a bridge between the foundational concepts of wavelet theory and its practical applications, offering a condensed and accessible introduction to these topics.
This volume combines several streams of wavelet theory, focusing on three core areas:
1. **Wavelet Theory**: The mathematical construction and theoretical foundations of wavelets, focusing on their ability to approximate functions and surfaces in an efficient and flexible manner. This section delves into the results and principles behind wavelet theory, which may be scattered throughout the research literature, but are presented here in a concise and digestible format.
2. **Applications in Data Compression and Signal Processing**: The book explores how wavelets are applied in practical areas, especially in the fields of data compression and signal/image processing. Wavelets have proven to be invaluable in tasks such as reducing the size of large datasets, performing detailed signal analysis, and compressing images without significant loss of quality.
3. **Nonparametric Statistical Methods**: Wavelet theory's application to statistical problems is an area of growing importance. The book covers how wavelets can be employed in nonparametric statistical analysis, where traditional methods may be inadequate. This approach offers a new perspective on solving statistical problems, particularly those that involve irregular data or complex structures.
In addition to theoretical concepts, the book includes practical guidance on how to use wavelet techniques with available software code. This makes it suitable not only for researchers looking to deepen their understanding of wavelets but also for practitioners who wish to implement wavelet methods in their own work.
**Key Features:**
- **Comprehensive introduction**: Ideal for those new to wavelet theory, offering a clear and accessible introduction to the subject.
- **Condensed theoretical results**: A selection of essential theoretical results, many of which are scattered across the research literature, presented in a compact format for easy understanding.
- **Practical applications**: Demonstrates the practical use of wavelets in data compression, signal/image processing, and nonparametric statistics.
- **Software code integration**: Guidance on using available software to implement wavelet methods, making the book both a theoretical and practical resource.
**Audience:**
- **Researchers**: Those interested in the theoretical foundations of wavelets and their applications in various fields, including signal processing, data compression, and statistical analysis.
- **Practitioners**: Engineers, data scientists, and others who need to apply wavelet methods to real-world problems will find this book a useful resource.
- **Students**: Those studying mathematics, statistics, or engineering who wish to understand wavelets and their diverse applications in modern computational methods.
**Conclusion:**
*Wavelets: Theory and Applications* provides an accessible yet detailed guide to the theory and applications of wavelet analysis. Whether you are a novice looking to understand the fundamentals or a practitioner seeking to apply wavelets to real-world problems, this book offers a thorough yet concise introduction to the subject. By blending theoretical insights with practical software applications, it opens the door to a wide range of possibilities for researchers and professionals alike. [/content]
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