1st Edition

Wavelets from a Statistical Perspective

By Maarten Jansen Copyright 2022
346 Pages 84 B/W Illustrations
by Chapman & Hall

346 Pages 84 B/W Illustrations
by Chapman & Hall

346 Pages 84 B/W Illustrations
by Chapman & Hall

Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced... Read more

Chapter 1 Wavelets: nonlinear processing in multiscale sparsity

Chapter 2 Wavelet building blocks

Chapter 3 Using lifting for the design of a wavelet transform

Chapter 4 Wavelet transforms from factored refinement schemes

Chapter 5 Dyadic wavelets

Chapter 6 Dyadic wavelet design in the frequency domain

Chapter 7 Design of dyadic wavelets

Chapter 8 Approximation in a wavelet basis

Chapter 9 Overcomplete wavelet transforms

Chapter 10 Two-dimensional wavelet transforms

Chapter 11 The multiscale local polynomial transform

Chapter 12 Estimation in a wavelet basis

Outlook

References

Subject Index

List of Recurrent symbols

Biography

Maarten Jansen is professor at the Mathematics and Computer Science departments of the Université libre de Bruxelles.

"The book is a very much welcome addition to the vast literature on wavelets... Overall, the text is a very handy account of more modern take on wavelets with some statistical flavour. It can serve as a good textbook on wavelets or become a valuable reference companion given that one spends enough time on an initial, systematic study of the contents."

Krzysztof Podgórski, Lund University, Sweden, International Statistical Review, 2022.