Applied Mathematics Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications - Chui, Charles K.; Jiang, Qingtang; SpringerLink (Online service) (Paris : Atlantis Press : Imprint: Atlantis Press, 2013)
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 (3z(Bfrequency(3y (Bof the data, providing valuable information for, e.g. data compression and noise removal. Furthermore, a special emphasis is also put on the concept of (3z(Bwavelets(3y (Bin connection with the (3z(Bmulti-scale(3y (Bstructure 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.s
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.
Keywords: Mathematics; Computer vision; Statistics; Engineering design; Mathematics; Applications of Mathematics; Information and Communication, Circuits; Statistics, general; Computer Imaging, Vision, Pattern Recognition and Graphics; Engineering Design