Spline and Spline Wavelet Methods with Applications to Signal and Image Processing: Volume I: Periodic Splines

Spline and Spline Wavelet Methods with Applications to Signal and Image Processing: Volume I: Periodic Splines


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This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications.It is done with discreteand polynomialperiodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based onZak transform and onSpline Harmonic Analysis (SHA) methodology.SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fouriertransform. SHA reduces the designof different spline types such as splines, spline wavelets (SW), wavelet frames (SWF)and wavelet packets (SWP)and their manipulations by simple operations. Digital filters, producedby waveletsdesign process, give birth tosubdivision schemes. Subdivision schemes enable to performfast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and imagesup sampling. In addition tothe design of a diverse library of splines, SW, SWP and SWF, this book describes theirapplications topractical problems. The applications include up sampling, image denoising,recovery from blurred images, hydro-acoustic target detection, to name a few. TheSWFare utilized for imagerestoration that was degraded by noise, blurring and loss of significant number of pixels. The bookis accompanied byMatlab based software that demonstrates andimplements all the presented algorithms. The book combines extensive theoretical exposurewith detailed description of algorithms, applications and software.

The Matlab software can be downloaded from http://extras.springer.com

Product Details

ISBN-13: 9789401789257
Publisher: Springer Netherlands
Publication date: 04/09/2014
Edition description: 2014
Pages: 496
Product dimensions: 6.10(w) x 9.25(h) x 0.05(d)

About the Author

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 nume

rical 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 thesis" at St. Petersburg University. He received Dr. Sci. degree (habilitation) on Comput. Math. from Siberia Branch of Acad. Sci. USSR. Took positions from Lecturer at Pedagogical Univ., St. Petersburg, to full Professor at St.-Petersburg Military Institute for Construction Engineering. In 1995 he moved to Israel, where took positions from Researcher to Associate Professor at the School of Computer Science, TelAviv University, Israel. Currently, he is retired from the Associate Professor position and is working as a Researcher at the RAMOT company, which is a research branch of Tel Aviv University. Starting from 2010 he is working as a Senior Researcher at the Dept. of Mathematical Information Technology, University of Jyvaskyla, Finland.

Fields of research:|
Wavelet and Frame Analysis, Approximation Theory, Signal and Image Processing, Hyperspectral Processing, Geophysics, Pattern Recognition, Target Detection, Medical Imaging.


ted in many industrial research projects in Israel and Finland in cooperation with the Israeli Ministries of Defense and Sciences and with companies such as Paradigm Geophysical Ltd, Waves Audio Ltd, Bar-Kal Systems Engineering Ltd, ELTA Systems Ltd., Applied Materials, Orbotech, Nova, ElOp, Elta, Metso, Patria Aviation, TietoSaab.

Table of Contents

1 Introduction: Signals and transforms

2 Introduction: Periodic filters and filter banks

3 Mixed circular convolutions and Zak transforms

4 Periodic polynomial splines

5 Polynomial smoothing splines

6 Calculation of splines values by subdivision

7 Spline algorithms for deconvolution and inversion of heat equation

8 Periodic spline wavelets and wavelet packets

9 Discrete-time periodic wavelet packets

10 Deconvolution by regularized matching pursuit

11 Block-based inversion of the heat equations

12 Hydro-acoustic target detection

13 Periodic discrete splines

14 Discrete periodic spline wavelets and wavelet Packets

15 Biorthogonal wavelet transforms

16 Biorthogonal wavelet transforms originating from splines

17 Wavelet frames generated by spline based p-filter banks

18 Application of periodic frames to image restoration

Appendix: Guide to SplineSoftP



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