Applied Mathematics: Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications

✍ Scribed by Charles K. Chui, Qingtang Jiang (auth.)

• Publisher: Atlantis Press
• Year: 2013
• Tongue: English
• Leaves: 567
• Series: Mathematics Textbooks for Science and Engineering 2
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xxii
Linear Spaces....Pages 1-62
Linear Analysis....Pages 63-113
Spectral Methods and Applications....Pages 115-169
Frequency-Domain Methods....Pages 171-205
Data Compression....Pages 207-262
Fourier Series....Pages 263-316
Fourier Time-Frequency Methods....Pages 317-377
Wavelet Transform and Filter Banks....Pages 379-432
Compactly Supported Wavelets....Pages 433-498
Wavelet Analysis....Pages 499-546
Back Matter....Pages 547-551

✦ Subjects

Applications of Mathematics; Information and Communication, Circuits; Statistics, general; Computer Imaging, Vision, Pattern Recognition and Graphics; Engineering Design