Spline and Spline Wavelet Methods with Applications to Signal and Image Processing.Vol.2

Preface 1 Introduction: Signals and Transforms 2 Introduction: Digital Filters and Filter Banks 3 Mixed Convolutions and Zak Transforms 4 Non-Periodic Polynomial Splines 5 Quasi-Interpolating and Smoothing Local Splines 6 Cubic Local Splines on Non-Uniform Grid 7 Splines Computation by Subdivision 8 Polynomial Spline-Wavelets 9 Non-Periodic Discrete Splines 10 Non-Periodic Discrete-Spline Wavelets 11 Biorthogonal Wavelet Transforms 12 Biorthogonal Wavelet Transforms Originating from Splines 13 Data Compression Using Wavelet and Local Cosine Transforms 14 Wavelet Frames Generated by Perfect Reconstruction Filter Banks 15 Biorthogonal Multiwavelets Originated from Hermite Splines 16 Multiwavelet Frames Originated from Hermite Splines Appendix A - Guide to Spline SoftN Glossary Index

Amir Averbuch is a professor of Computer since 1987 in the School of Computer Science, Tel Aviv University. He is also the founder and CSO of ThetaRay LTD. He got his B.Sc and M.Sc in mathematics from the Hebrew University in Jerusalem in 1968, 1975, respectively, and a PhD in computer Science from Columbia University in 1983. He has over 30 years of experience in research and development in academia and industry. Between 1977-1986 he was research staff member in IBM T.J. Watson Research Center, Yorktown Heights. New York. His research interests include applied and computational harmonic analysis, big data processing and analysis, cyber security, signal/image processing, Wavelets, scientific computing He was visiting professor in many places. He has supervised 102 M.Sc. 19 PhD and 13 post-doc students. He has published 198 papers in refereed journals, 170 papers in conferences, 10 chapters in books and 20 patents.

Pekka Neittaanmäki is Professor in Scientific Computing and Dean of the Faculty of Information Technology and Head of COMAS (Computing and Mathematical Sciences) Graduate School at the University of Jyväskylä, Visiting Professor at the Tokyo Institute of Technology, Japan, and Adjoint Professor at the University of Houston, USA. His research interests are mathematical and numerical modeling, signal analysis, data analysis, optimization, and optimal control. He is the author or co-author of more than 300 publications in various parts of numerical analysis and applied mathematics including 14 books. He has supervised more than 80 PhD theses. He has participated in many industrial projects in Finland and Europe including among others paper machine, telecommunication, process industry as well as medical diagnostics applications.

Valery A. Zheludev, received his M.S. degree on Math. Physics from St. Petersburg State University, Russia. He received Ph.D. degree on Math. Physics from Steklov Math. Inst. of Acad. Sci. USSR and the prize "For the best Ph.D

"This book is the second volume in an extensive treatment of splines, spline wavelets, and their applications to signal and image processing. ... The book provides a self-contained and extensive exposition of the fundamentals of both splines and wavelets transforms ... . This book belongs on the shelf of every researcher in signal and image processing. ... a valuable supplement for graduate level courses." (James Stephan Walker, Mathematical Reviews, July, 2016)

"This excellent monograph provides a universal toolbox (with numerous MATLAB codes) for methods with polynomial resp. discrete splines and spline wavelets and corresponding applications in signal and image processing. ... This book is well-written and contains many examples and figures. It is very convenient for broad readership of graduate students and researchers in applied mathematics, computer science, physics, and engineering. Doubtless, this nice book will stimulate further applications of spline wavelet methods." (Manfred Tasche, zbMATH 1338.65032, 2016)