Functional Analysis Harmonic Analysis And Image Processing
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| Author | : Michael Cwikel |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 422 |
| Release | : 2017-07-26 |
| Genre | : Computers |
| ISBN | : 1470428369 |
This volume is dedicated to the memory of Björn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Björn made important contributions. Those areas include harmonic analysis, image processing, and functional analysis, which are of course interrelated in many significant and productive ways. Among the contributors are some of the world's leading experts in these areas. With its combination of research papers and surveys, this book may become an important reference and research tool. This book should be of interest to advanced graduate students and professional researchers in the areas of functional analysis, harmonic analysis, image processing, and approximation theory. It combines articles presenting new research with insightful surveys written by foremost experts.
| Author | : Tony F. Chan |
| Publisher | : SIAM |
| Total Pages | : 414 |
| Release | : 2005-09-01 |
| Genre | : Computers |
| ISBN | : 089871589X |
This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.
| Author | : Kristian Bredies |
| Publisher | : Springer |
| Total Pages | : 481 |
| Release | : 2019-02-06 |
| Genre | : Mathematics |
| ISBN | : 3030014584 |
This book addresses the mathematical aspects of modern image processing methods, with a special emphasis on the underlying ideas and concepts. It discusses a range of modern mathematical methods used to accomplish basic imaging tasks such as denoising, deblurring, enhancing, edge detection and inpainting. In addition to elementary methods like point operations, linear and morphological methods, and methods based on multiscale representations, the book also covers more recent methods based on partial differential equations and variational methods. Review of the German Edition: The overwhelming impression of the book is that of a very professional presentation of an appropriately developed and motivated textbook for a course like an introduction to fundamentals and modern theory of mathematical image processing. Additionally, it belongs to the bookcase of any office where someone is doing research/application in image processing. It has the virtues of a good and handy reference manual. (zbMATH, reviewer: Carl H. Rohwer, Stellenbosch)
| Author | : Stephan Dahlke |
| Publisher | : Birkhäuser |
| Total Pages | : 268 |
| Release | : 2015-09-12 |
| Genre | : Mathematics |
| ISBN | : 3319188631 |
This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.
| Author | : David V. Cruz-Uribe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 316 |
| Release | : 2013-02-12 |
| Genre | : Mathematics |
| ISBN | : 3034805489 |
This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.
| Author | : Michael Cwikel |
| Publisher | : |
| Total Pages | : |
| Release | : 2017 |
| Genre | : Fourier analysis |
| ISBN | : 9781470441661 |
This volume is dedicated to the memory of Björn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Björn made important contributions. Those areas include harmonic analysis, image processing, and functional analysis, which are of course interrelated in many significant and productive ways. Among the contributors are some of the world's leading experts in these areas. With its combination of research papers and surveys, this book may become an important reference and research tool. This book should be of interest to advanced graduate.
| Author | : Arch W. Naylor |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 648 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : 9780387950013 |
This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.
| Author | : Akram Aldroubi |
| Publisher | : Springer Nature |
| Total Pages | : 335 |
| Release | : 2019-11-26 |
| Genre | : Mathematics |
| ISBN | : 3030323536 |
This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.
| Author | : Bin Han |
| Publisher | : Springer |
| Total Pages | : 750 |
| Release | : 2018-01-04 |
| Genre | : Mathematics |
| ISBN | : 3319685309 |
Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide. As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises. Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets. Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.
| Author | : Tim Olson |
| Publisher | : Birkhäuser |
| Total Pages | : 310 |
| Release | : 2017-11-20 |
| Genre | : Mathematics |
| ISBN | : 1493973932 |
The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medi cal imaging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects. Illuminating videos are available on Springer.com and Link.Springer.com that present animated visualizations of several concepts. The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis.
