This Second Edition continues to distill the abstract ideas of wavelet theory to a level accessible to undergraduates and at the same time, introduced readers to the theory via an applications first approach. With extensive graphical displays, this self-contained book integrates concepts from calculus and linear algebra into the construction of wavelet transformations and their various applications, including data compression, edge detection in images, and signal and image denoising. The book begins with a cursory look at wavelet transformation development and illustrates its allure in digital signal and image applications. Next, a chapter on digital image basics, quantitative and qualitative measures, and Huffman coding equips readers with the tools necessary to develop a comprehensive understanding of the applications. Subsequent chapters discuss the Fourier series, convolution, and filtering, as well as the Haar wavelet transform to introduce image compression and image edge detection. The book also reviews the JPEG2000 image compression standard and the basic JPEG2000 algorithm. The new edition has been thoroughly revised to include new applications including image segmentation and the FBI Wavelet/Scalar Quantization Method, and new tools needed to model solutions to problems are presented, such as color space conversions, data encoding, and data quantization. Expanded coverage of Fourier series provides readers with an overview of the effects that phase shifts, derivatives, and modulation have on Fourier coefficients. New chapters on lifting and wavelet packets are also included. Updated versions of the DiscreteWaveletes package/toolbox for Mathematica and MATLAB have been incorporated, and a related website features final projects material.
