Wavelet Analysis

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 discrete transform integer algorithms. 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 denosing/restoration, image image enhancement, transient feature detection, numerical solution of partial differential equations, and solving ill-conditioned Toeplitz system. The book is intended for senior undergraduate students and graduate students.