Fourier Methods in Imaging 1st Edition by Roger L. Easton Jr. (PDF)

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

User’s Reviews

Editorial Reviews: Review “Overall, this is an excellent text, appropriate for the graduate student approaching this material for the first time, and for the seasoned professional looking for an up-to-date reference.” (Journal of Electronic Imaging, 1 April 2011) “This comprehensive textbook represents a practical review of Fourier techniques in imaging methods. It will be very useful for graduate students (in engineering, science, computer science, and applied mathematics) as well as engineers interested in linear imaging systems.” (Zentralblatt Math, 2010) From the Inside Flap 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. From the Back Cover 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. About the Author Professor Roger L. Easton, Jr Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology Professor Easton teaches undergraduate and graduate courses in linear systems, optical imaging, and digital image processing at Rochester Institute of Technology. He received a B.S. degree in Astronomy from Haverford College, an M.S. in physics from the University of Maryland, and an M.S. and Ph.D. degree in Optical Sciences from the University of Arizona. His research interests include the application of digital image processing to text documents and manuscripts. He has contributed to work on the Dead Sea Scrolls and is now part of an imaging team helping scolars to read the original Archimiedes Palimpsest. Professor Easton also conducts research into optical signal processing and computer-generated holography, publishing articles on both. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Roger Easton’s “Fourier Methods in Imaging” is a monolithic ensemble of mathematics as it pertains to the science of imaging, and somehow, the first edition text offers a remarkably thorough and polished presentation of the subject matter. In similar fashion to the several Linear Algebra texts by Gilbert Strang, here we find a wonderful teaching style in which underlying theory is accompanied by meticulously organized examples, all building a clear progression of the many complex concepts in the book. Whether investigating subtleties between continuous and discrete signal problems, filter design for digital image processing, or the mathematical foundation for optical image formation, content in “Fourier Methods in Imaging” is presented in an order that encourages the reader to learn piece-by-piece, at his or her own pace. The author successfully encourages the reader to make critical leaps, such that the “Eureka!” moments are retained after reading. Moreover, the plethora of examples in no way hinders the use of the text as a solid reference guide for those already acquainted with the material. To be quite honest, I have learned something new every time I have referenced this gem!After clearly offering my praise, I will refrain from stressing my opinion to keep the remainder of this review objective and discuss only content. The text aims to cover a great deal of material, and all 900+ pages seem necessary to really dive into the low-level details. The first few chapters offer a typical review of complex variables and Linear Algebra fundamentals necessary to develop the remainder of the content. Chapter 5 may be the most important chapter of the text, reviewing the three common linear imaging problems (direct, inverse, and analysis) and the familiar diagonalization process typically used for their simplification and understanding. This process is the change of basis that results from implementing the Fourier transform, which is then covered in great detail. The one-dimensional signal analysis found in most electrical engineering books is seamlessly extended to two-dimensional image analysis, and theoretical continuous case discussions are followed-up with their discrete counterparts. Spatial and frequency-domain filtering are covered and then reviewed in the context of inverse filtering for deconvolution and matched filtering for pattern recognition. With all of the necessary tools in place, Easton then dives into a foray of optical image formation, which serves as a nice (and concise) alternative to Joseph Goodman’s popular Fourier Optics book.Many disciplines have been integrated here. I highly recommend this text for electrical and optical engineers, physicists, and mathematicians interested in how imaging applications benefit from their respective fields. And if you already consider yourself an expert in Fourier Analysis because you have run canned-FFT algorithms in a high-level programming language, then this text is recommended to even greater extent (even if you only reference it to understand why you may want to apply a window to your signal before pressing that button!). “Fourier-Methods in Imaging” is probably best suited for graduate-level studies, but it could be easily partitioned into two or three advanced-undergraduate courses.This one belongs on your shelf – Thanks for reading!

⭐It is really a good book which everybody should be having especially the ones who are majoring in Electrical engineering, Imaging science, Mathematical science,Physics. I am majoring in Electrical engineering, I took the course as an elective course from the Imaging science, but I felt like we need this course to be in our department as a core course. The course opens your mind to a new things that you weren’t be seeing without it. So go for it.

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