Sampling Theory A Renaissance

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Sampling Theory, a Renaissance

Author : Götz E. Pfander
Publisher : Birkhäuser
ISBN 13 : 3319197495
Total Pages : 532 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Sampling Theory, a Renaissance by : Götz E. Pfander

Download or read book Sampling Theory, a Renaissance written by Götz E. Pfander and published by Birkhäuser. This book was released on 2015-12-08 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.

The Use of Frames in Sampling Theory

Author : Antonio García García
Publisher : Springer Nature
ISBN 13 : 3031632427
Total Pages : 314 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis The Use of Frames in Sampling Theory by : Antonio García García

Download or read book The Use of Frames in Sampling Theory written by Antonio García García and published by Springer Nature. This book was released on with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sampling: Theory and Applications

Author : Stephen D. Casey
Publisher : Springer Nature
ISBN 13 : 3030362914
Total Pages : 210 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Sampling: Theory and Applications by : Stephen D. Casey

Download or read book Sampling: Theory and Applications written by Stephen D. Casey and published by Springer Nature. This book was released on 2020-05-20 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory. Claude Shannon’s 100th birthday is also celebrated, including an introductory essay that highlights Shannon’s profound influence on the field. The topics covered include both theory and applications, such as: • Compressed sensing• Non-uniform and wave sampling• A-to-D conversion• Finite rate of innovation• Time-frequency analysis• Operator theory• Mobile sampling issues Sampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.

Lattice Point Identities and Shannon-Type Sampling

Author : Willi Freeden
Publisher : CRC Press
ISBN 13 : 1000757749
Total Pages : 287 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Lattice Point Identities and Shannon-Type Sampling by : Willi Freeden

Download or read book Lattice Point Identities and Shannon-Type Sampling written by Willi Freeden and published by CRC Press. This book was released on 2019-10-28 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice Point Identities and Shannon-Type Sampling demonstrates that significant roots of many recent facets of Shannon's sampling theorem for multivariate signals rest on basic number-theoretic results. This book leads the reader through a research excursion, beginning from the Gaussian circle problem of the early nineteenth century, via the classical Hardy-Landau lattice point identity and the Hardy conjecture of the first half of the twentieth century, and the Shannon sampling theorem (its variants, generalizations and the fascinating stories about the cardinal series) of the second half of the twentieth century. The authors demonstrate how all these facets have resulted in new multivariate extensions of lattice point identities and Shannon-type sampling procedures of high practical applicability, thereby also providing a general reproducing kernel Hilbert space structure of an associated Paley-Wiener theory over (potato-like) bounded regions (cf. the cover illustration of the geoid), as well as the whole Euclidean space. All in all, the context of this book represents the fruits of cross-fertilization of various subjects, namely elliptic partial differential equations, Fourier inversion theory, constructive approximation involving Euler and Poisson summation formulas, inverse problems reflecting the multivariate antenna problem, and aspects of analytic and geometric number theory. Features: New convergence criteria for alternating series in multi-dimensional analysis Self-contained development of lattice point identities of analytic number theory Innovative lattice point approach to Shannon sampling theory Useful for students of multivariate constructive approximation, and indeed anyone interested in the applicability of signal processing to inverse problems.

Sampling, Approximation, and Signal Analysis

Author : Stephen D. Casey
Publisher : Springer Nature
ISBN 13 : 3031411307
Total Pages : 580 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Sampling, Approximation, and Signal Analysis by : Stephen D. Casey

Download or read book Sampling, Approximation, and Signal Analysis written by Stephen D. Casey and published by Springer Nature. This book was released on 2024-01-04 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings – of which he was a Founding Member – is also included. The remaining articles are grouped into four sections – classical sampling, theoretical extensions, frame theory, and applications of sampling theory – and explore Higgins’ contributions to these areas, as well as some of the latest developments.

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555561
Total Pages : 512 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by : Isaac Pesenson

Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Metrics, Norms, Inner Products, and Operator Theory

Author : Christopher Heil
Publisher : Birkhäuser
ISBN 13 : 3319653229
Total Pages : 374 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Metrics, Norms, Inner Products, and Operator Theory by : Christopher Heil

Download or read book Metrics, Norms, Inner Products, and Operator Theory written by Christopher Heil and published by Birkhäuser. This book was released on 2018-08-28 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another. With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.” Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of lp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle. The text is constructed in such a way that instructors have the option whether to include more advanced topics. Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course. Instructors have several options for building a course around the text depending on the level and interests of their students. Key features: Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter. Suitable for undergraduate-level courses; no familiarity with measure theory is required. Extensive exercises complement the text and provide opportunities for learning by doing. A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.

Compressed Sensing and its Applications

Author : Holger Boche
Publisher : Birkhäuser
ISBN 13 : 3319698028
Total Pages : 402 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Compressed Sensing and its Applications by : Holger Boche

Download or read book Compressed Sensing and its Applications written by Holger Boche and published by Birkhäuser. This book was released on 2018-01-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing. Article authors address their techniques for solving the problems of compressed sensing, as well as connections to related areas like detecting community-like structures in graphs, curbatures on Grassmanians, and randomized tensor train singular value decompositions. Some of the novel applications covered include dimensionality reduction, information theory, random matrices, sparse approximation, and sparse recovery. This book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering, as well as other applied scientists exploring the potential applications for the novel methodology of compressed sensing. An introduction to the subject of compressed sensing is also provided for researchers interested in the field who are not as familiar with it.

Advances in Sampling Theory-Ratio Method of Estimation

Author : Hulya Cingi
Publisher : Bentham Science Publishers
ISBN 13 : 1608050122
Total Pages : 129 pages
Book Rating : 4.6/5 (8 download)

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Book Synopsis Advances in Sampling Theory-Ratio Method of Estimation by : Hulya Cingi

Download or read book Advances in Sampling Theory-Ratio Method of Estimation written by Hulya Cingi and published by Bentham Science Publishers. This book was released on 2009-08-11 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Ratio Method of Estimation - This is an ideal textbook for researchers interested in sampling methods, survey methodologists in government organizations, academicians, and graduate students in statistics, mathematics and biostatistics. This textbook makes"

Transionospheric Synthetic Aperture Imaging

Author : Mikhail Gilman
Publisher : Birkhäuser
ISBN 13 : 3319521276
Total Pages : 468 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Transionospheric Synthetic Aperture Imaging by : Mikhail Gilman

Download or read book Transionospheric Synthetic Aperture Imaging written by Mikhail Gilman and published by Birkhäuser. This book was released on 2017-04-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This landmark monograph presents the most recent mathematical developments in the analysis of ionospheric distortions of SAR images and offers innovative new strategies for their mitigation. As a prerequisite to addressing these topics, the book also discusses the radar ambiguity theory as it applies to synthetic aperture imaging and the propagation of radio waves through the ionospheric plasma, including the anisotropic and turbulent cases. In addition, it covers a host of related subjects, such as the mathematical modeling of extended radar targets (as opposed to point-wise targets) and the scattering of radio waves off those targets, as well as the theoretical analysis of the start-stop approximation, which is used routinely in SAR signal processing but often without proper justification. The mathematics in this volume is clean and rigorous – no assumptions are hidden or ambiguously stated. The resulting work is truly interdisciplinary, providing both a comprehensive and thorough exposition of the field, as well as an accurate account of a range of relevant physical processes and phenomena. The book is intended for applied mathematicians interested in the area of radar imaging or, more generally, remote sensing, as well as physicists and electrical/electronic engineers who develop/operate spaceborne SAR sensors and perform the data processing. The methods in the book are also useful for researchers and practitioners working on other types of imaging. Moreover, the book is accessible to graduate students in applied mathematics, physics, engineering, and related disciplines. Praise for Transionospheric Synthetic Aperture Imaging: “I perceive that this text will mark a turning point in the field of synthetic aperture radar research and practice. I believe this text will instigate a new era of more rigorous image formation relieving the research, development and practitioner communities of inconsistent physical assumptions and numerical approaches.” – Richard Albanese, Senior Scientist, Albanese Defense and Energy Development LLC

Advances in Microlocal and Time-Frequency Analysis

Author : Paolo Boggiatto
Publisher : Springer Nature
ISBN 13 : 3030361381
Total Pages : 533 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Advances in Microlocal and Time-Frequency Analysis by : Paolo Boggiatto

Download or read book Advances in Microlocal and Time-Frequency Analysis written by Paolo Boggiatto and published by Springer Nature. This book was released on 2020-03-03 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.

Modulation Spaces

Author : Árpád Bényi
Publisher : Springer Nature
ISBN 13 : 1071603329
Total Pages : 177 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Modulation Spaces by : Árpád Bényi

Download or read book Modulation Spaces written by Árpád Bényi and published by Springer Nature. This book was released on 2020-02-22 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.

Harmonic and Applied Analysis

Author : Filippo De Mari
Publisher : Springer Nature
ISBN 13 : 3030866645
Total Pages : 316 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Harmonic and Applied Analysis by : Filippo De Mari

Download or read book Harmonic and Applied Analysis written by Filippo De Mari and published by Springer Nature. This book was released on 2021-12-13 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science. This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on Applied Harmonic Analysis, held at the University of Genova in 2017 and 2019. Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers. Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.

Mathematical Image Processing

Author : Kristian Bredies
Publisher : Springer
ISBN 13 : 3030014584
Total Pages : 481 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Mathematical Image Processing by : Kristian Bredies

Download or read book Mathematical Image Processing written by Kristian Bredies and published by Springer. This book was released on 2019-02-06 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)

Excursions in Harmonic Analysis, Volume 6

Author : Matthew Hirn
Publisher : Springer Nature
ISBN 13 : 3030696375
Total Pages : 444 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Excursions in Harmonic Analysis, Volume 6 by : Matthew Hirn

Download or read book Excursions in Harmonic Analysis, Volume 6 written by Matthew Hirn and published by Springer Nature. This book was released on 2021-09-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.

Harmonic Analysis and Partial Differential Equations

Author : Justin Feuto
Publisher : Springer Nature
ISBN 13 : 3031663756
Total Pages : 273 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Harmonic Analysis and Partial Differential Equations by : Justin Feuto

Download or read book Harmonic Analysis and Partial Differential Equations written by Justin Feuto and published by Springer Nature. This book was released on with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt:

From Classical Analysis to Analysis on Fractals

Author : Patricia Alonso Ruiz
Publisher : Springer Nature
ISBN 13 : 3031378008
Total Pages : 294 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis From Classical Analysis to Analysis on Fractals by : Patricia Alonso Ruiz

Download or read book From Classical Analysis to Analysis on Fractals written by Patricia Alonso Ruiz and published by Springer Nature. This book was released on 2023-11-25 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.