Continuous Wavelet Transform

The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject.

This book is intended to attract the attention of practitioners and researchers in the academia and industry interested in challenging paradigms of wavelets and its application with an emphasis on the recent technological developments. The book highlights the current research in the usage of wavelets in different areas such as biomedical analysis, fringe-pattern analysis, image applications, network data transfer applications, and optical measurement techniques.

Intuitions behind digital signal processing

Recently there has been intense research activity on the subject of wavelet and subband theory. Experts in diverse fields such as mathematics, physics, electrical engineering, and image processing have provided original and pioneering works and results. But this diversity, while rich and productive, has led to a sense of fragmentation, especially to those new to the field and to nonspecialists who are trying to understand the connections between the different aspects of wavelet and subband theory. `Wavelets and Subbands' is designed to present an understanding of wavelets and their development from a continuous-domain transformation to a frame representation and finally to multiresolution analysis tools such as subband decomposition. The book presents a theoretical understanding of the subject that is intertwined with practical examples and applications of wavelets in ultrasonic and biomedical domains. There is special emphasis on applications in communications, compression, and image processing.

This book surveys the application of the recently developed technique of the wavelet transform to a wide range of physical fields, including astrophysics, turbulence, meteorology, plasma physics, atomic and …