Gabor and wavelet analyses have found widespread applications in signal analysis, image processing and many other information-related areas. Both deliver representations that are simultaneously local in time and in frequency. Due to their significance and success in practical applications, they formed some of the core topics of the program "Mathematics and Computation in Imaging Science and Information Processing", which was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004. As part of the program, tutorial lectures were conducted by international experts, and they covered a wide spectrum of topics in mathematical image, signal and information processing.This volume includes exposition articles by the tutorial speakers on the foundations of Gabor analysis, subband filters and wavelet algorithms, and operator-theoretic interpolation of wavelets and frames. It also presents research papers on Gabor analysis, written by specialists in their respective areas. The volume takes graduate students and researchers new to the field on a valuable learning journey from introductory Gabor and wavelet analyses to advanced topics of current research.
A Guided Tour from Linear Algebra to the Foundations of Gabor Analysis (H G Feichtinger et al.); Some Iterative Algorithms to Compute Canonical Windows for Gabor Frames (A J E M Janssen); Gabor Analysis, Noncommutative Tori and Feichtinger's Algebra (F Luef); Unitary Matrix Functions, Wavelet Algorithms, and Structural Properties of Wavelets (P E T Jorgensen); Unitary Systems, Wavelet Sets, and Operator-Theoretic Interpolation of Wavelets and Frames (D R Larson).