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Author: Ronald Bracewell
Publisher: Springer Science & Business Media
ISBN: 1441989633
Category : Technology & Engineering
Languages : en
Pages : 702
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Book Description
As Lord Kelvin said, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." This has remained durable knowledge for a century, and has extended its applicability to topics as diverse as medical imaging (CT scanning), the presentation of images on screens and their digital transmission, remote sensing, geophysical exploration, and many branches of engineering. Fourier Analysis and Imaging is based on years of teaching a course on the Fourier Transform at the senior or early graduate level, as well as on Prof. Bracewell's 1995 text Two-Dimensional Imaging. It is an excellent textbook and will also be a welcome addition to the reference library of those many professionals whose daily activities involve Fourier analysis in its many guises.
Author: Ronald Bracewell
Publisher: Springer Science & Business Media
ISBN: 1441989633
Category : Technology & Engineering
Languages : en
Pages : 702
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Book Description
As Lord Kelvin said, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." This has remained durable knowledge for a century, and has extended its applicability to topics as diverse as medical imaging (CT scanning), the presentation of images on screens and their digital transmission, remote sensing, geophysical exploration, and many branches of engineering. Fourier Analysis and Imaging is based on years of teaching a course on the Fourier Transform at the senior or early graduate level, as well as on Prof. Bracewell's 1995 text Two-Dimensional Imaging. It is an excellent textbook and will also be a welcome addition to the reference library of those many professionals whose daily activities involve Fourier analysis in its many guises.
Author: Roger L. Easton Jr.
Publisher: John Wiley & Sons
ISBN: 1119991862
Category : Technology & Engineering
Languages : en
Pages : 1005
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Book Description
Fourier Methods in Imaging introduces the mathematical tools for modeling linear imaging systems to predict the action of the system or for solving for the input. The chapters are grouped into five sections, the first introduces the imaging “tasks” (direct, inverse, and system analysis), the basic concepts of linear algebra for vectors and functions, including complex-valued vectors, and inner products of vectors and functions. The second section defines "special" functions, mathematical operations, and transformations that are useful for describing imaging systems. Among these are the Fourier transforms of 1-D and 2-D function, and the Hankel and Radon transforms. This section also considers approximations of the Fourier transform. The third and fourth sections examine the discrete Fourier transform and the description of imaging systems as linear "filters", including the inverse, matched, Wiener and Wiener-Helstrom filters. The final section examines applications of linear system models to optical imaging systems, including holography. Provides a unified mathematical description of imaging systems. Develops a consistent mathematical formalism for characterizing imaging systems. Helps the reader develop an intuitive grasp of the most common mathematical methods, useful for describing the action of general linear systems on signals of one or more spatial dimensions. Offers parallel descriptions of continuous and discrete cases. Includes many graphical and pictorial examples to illustrate the concepts. This book helps students develop an understanding of mathematical tools for describing general one- and two-dimensional linear imaging systems, and will also serve as a reference for engineers and scientists
Author: Tim Olson
Publisher: Birkhäuser
ISBN: 1493973932
Category : Mathematics
Languages : en
Pages : 310
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Book Description
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.
Author: Okan K. Ersoy
Publisher: John Wiley & Sons
ISBN: 0470084995
Category : Technology & Engineering
Languages : en
Pages : 433
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Book Description
This book presents current theories of diffraction, imaging, and related topics based on Fourier analysis and synthesis techniques, which are essential for understanding, analyzing, and synthesizing modern imaging, optical communications and networking, as well as micro/nano systems. Applications covered include tomography; magnetic resonance imaging; synthetic aperture radar (SAR) and interferometric SAR; optical communications and networking devices; computer-generated holograms and analog holograms; and wireless systems using EM waves.
Author: Mehrdad Soumekh
Publisher: Prentice Hall
ISBN:
Category : Mathematics
Languages : en
Pages : 586
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Book Description
The past forty years have seen a number of imaging modalities developed for radar, sonar, diagnostic medicine, geophysical and celestial exploration, and non-destructive testing. Now, for those involved in designing and developing information processing tools for these imaging systems, author Mehrdad Soumekh offers in-depth coverage of diverse issues such as physical and mathematical modeling of the problem, signal processing, reconstruction, analysis of resolution and system parameter constraints, hardware structure used for data acquisition, and the overall imaging system block diagram (signal flow-chart) indicating how the acquired data are processed to yield the final reconstructed image. Fourier Array Imaging introduces the spatial Doppler phenomenon in conjunction with the most primitive signal processing tools and systems used in array imaging; presents terminologies and tools for two-dimensional signal processing; treats specific array imaging systems via the unifying framework of spatial Doppler processing, including phased-array imaging, synthetic aperture array (SAR and ISAR) imaging, passive array imaging, and bistatic array imaging with emphasis on transmission imaging problems of diagnostic medicine and geophysical exploration; devotes coverage to the analysis of resolution anticipated in an imaging system and to the constraints that are instrumental for selecting parameters of an imaging system; describes some of the classical methods used for image formation in array imaging systems and relates them to the spatial Doppler-based imaging via certain approximations.
Author: Ronald Newbold Bracewell
Publisher:
ISBN:
Category : Image processing
Languages : en
Pages : 716
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Book Description
Author: Peter Kuchment
Publisher: SIAM
ISBN: 1611973287
Category : Computers
Languages : en
Pages : 238
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Book Description
This book surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography. The Radon Transform and Medical Imaging emphasizes mathematical techniques and ideas arising across the spectrum of medical imaging modalities and explains important concepts concerning inversion, stability, incomplete data effects, the role of interior information, and other issues critical to all medical imaging methods. For nonexperts, the author provides appendices that cover background information on notation, Fourier analysis, geometric rays, and linear operators. The vast bibliography, with over 825 entries, directs readers to a wide array of additional information sources on medical imaging for further study.
Author: Kedar Khare
Publisher: John Wiley & Sons
ISBN: 1118900340
Category : Technology & Engineering
Languages : en
Pages : 312
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Book Description
This book covers both the mathematics of inverse problems and optical systems design, and includes a review of the mathematical methods and Fourier optics. The first part of the book deals with the mathematical tools in detail with minimal assumption about prior knowledge on the part of the reader. The second part of the book discusses concepts in optics, particularly propagation of optical waves and coherence properties of optical fields that form the basis of the computational models used for image recovery. The third part provides a discussion of specific imaging systems that illustrate the power of the hybrid computational imaging model in enhancing imaging performance. A number of exercises are provided for readers to develop further understanding of computational imaging. While the focus of the book is largely on optical imaging systems, the key concepts are discussed in a fairly general manner so as to provide useful background for understanding the mechanisms of a diverse range of imaging modalities.
Author: Charles L. Epstein
Publisher: SIAM
ISBN: 9780898717792
Category : Mathematics
Languages : en
Pages : 794
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Book Description
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.
Author: Timothy G. Feeman
Publisher: Springer Science & Business Media
ISBN: 0387927115
Category : Computers
Languages : en
Pages : 150
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Book Description
Medical imaging is a major part of twenty-first century health care. This introduction explores the mathematical aspects of imaging in medicine to explain approximation methods in addition to computer implementation of inversion algorithms.
