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Mathematics - Applications | Applied Mathematics

Applied Mathematics

Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications

Chui, Charles K., Jiang, Qingtang

2013, XXII, 551 p. 63 illus., 36 illus. in color.

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  • A comprehensive Applied Mathematics Textbook on the theory and methods with the central theme of information data processing, manipulation, and compression
  • Self-contained with minimum prerequisites from elementary linear algebra and calculus
  • A Text book for teaching at both undergraduate and beginning graduate levels 
  • Self-study for researchers in all disciplines of science and engineering
This textbook, apart from introducing the basic aspects of applied mathematics, focuses on recent topics such as information data manipulation, information coding, data approximation, data dimensionality reduction, data compression, time-frequency and time scale bases, image manipulation, and image noise removal. The methods treated in more detail include spectral representation and “frequency” of the data, providing valuable information for, e.g. data compression and noise removal. Furthermore, a special emphasis is also put on the concept of “wavelets” in connection with the “multi-scale” structure of data-sets. The presentation of the book is elementary and easily accessible, requiring only some knowledge of elementary linear algebra and calculus. All important concepts are illustrated with examples, and each section contains between 10 an 25 exercises. A teaching guide, depending on the level and discipline of instructions is included for classroom teaching and self-study.

Content Level » Graduate

Keywords » Algorithms and implementation schemes - Data manipulation and dimensionality reduction - Fourier and wavelet methods - Image and video compression - PDE

Related subjects » Applications - Image Processing - Mechanical Engineering - Statistics

Table of contents 

Linear Spaces.- Linerar Analysis.- Spectral Methods and Applications.- Frequency-Domain Methods.- Data Compression.- Fourier Series.- Fourier Time-Frequency Methods.- Wavelet Transform and Filter Banks.- Compactly Supported Wavelets.- Wavelet Analysis.

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