Mathematics of multilevel systems : data, scaling, images, signals, and fractals / Palle E T Jorgensen, The University of Iowa, USA; Myung-Sin Song, Southern Illinois University Edwardsville, USA.
Publisher:
World Scientific,
Copyright Date:
2023
Description:
xv, 253 pages : illustrations (some color) ; 24 cm
Includes bibliographical references (pages 239-249) and index.
Summary:
"This book presents the mathematics of wavelet theory and its applications in a broader sense, comprising entropy encoding, lifting scheme, matrix factorization, and fractals. It also encompasses image compression examples using wavelet transform and includes the principal component analysis which is a hot topic on data dimension reduction in machine learning. Readers will find equal coverage on the following three themes: a selection of practical projects and algorithms; the theory underpinning the subjects; the important interplay between theory and applications. The book entails a varied choice of diverse interdisciplinary themes. While the topics can be found in various parts of the pure and applied literature, this book fulfills the need for an accessible presentation which cuts across the fields. As the target audience is wide-ranging, a detailed and systematic discussion of issues involving infinite dimensions and Hilbert space is presented in later chapters on wavelets, transform theory and, entropy encoding and probability. For the problems addressed there, the case of infinite dimension will be more natural, and well-motivated"-- Provided by publisher.
Series:
Contemporary mathematics and its applications: monographs, expositions and lecture notes, 2591-7668 ; vol. 8
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.