This book could be divided into two parts i.e. fundamental wavelet transform theory and method and some important applications of wavelet transform. In the first part, as preliminary knowledge, the Fourier analysis, inner product space, the characteristics of Haar functions, and concepts of multi-resolution analysis, are introduced followed by a description on how to construct wavelet functions both multi-band and multi wavelets, and finally introduces the design of integer wavelets via lifting schemes and its application to integer transform algorithm. In the second part, many applications are discussed in the field of image and signal processing by introducing other wavelet variants such as complex wavelets, ridgelets, and curvelets. Important application examples include image compression, image denoising/restoration, image enhancement, digital watermarking, numerical solution of partial differential equations, and solving ill-conditioned Toeplitz system. The book is intended for senior undergraduate students and graduate students.

Preface / Overview of Fourier Analysis / Mathematical Foundation / Haar Wavelet Analysis / Multiresolution Analysis and Wavelets Design / M-band Wavelets and Multiwavelets / The Wavelet Based on the Lifting Scheme and Integer Discrete Transform / The Wavelet-based Image Compression / Wavelet Based Image Denoising and Enhancement / Ridgelets and its Applications / Application of Wavelet Transform in the Digital Watermarking / The Solution of PDE Based on Wavelets / The Solution of Ill-conditioned Symmetric Toeplitz Systems via Two-grid and Wavelet Methods.

Senior Undergraduate and Graduate Students