{"product_id":"fourier-methods-in-imaging-hardback-9780470689837","title":"Fourier Methods in Imaging (Hardback) 9780470689837","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFourier Methods in Imaging\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eRoger L. Easton Jr. (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470689837, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 May 2010\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e960 pages\u003cbr\u003e24.8 x 17.4 x 5.4 cm, 1.758 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"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)  \u003cp\u003e \"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)\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003ci\u003eFourier Methods in Imaging\u003c\/i\u003e 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.\u003cbr\u003e \u003cbr\u003e   \u003cul\u003e \u003cli\u003eProvides a unified mathematical description of imaging systems.\u003c\/li\u003e \u003cli\u003eDevelops a consistent mathematical formalism for characterizing imaging systems.\u003c\/li\u003e \u003cli\u003eHelps 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.\u003c\/li\u003e \u003cli\u003eOffers parallel descriptions of continuous and discrete cases.\u003c\/li\u003e \u003cli\u003eIncludes many graphical and pictorial examples to illustrate the concepts.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThis 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\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cb\u003eSeries Editor’s Preface.\u003c\/b\u003e  \u003cp\u003e\u003cb\u003ePreface.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Signals, Operators, and Imaging Systems.\u003c\/p\u003e \u003cp\u003e1.2 The Three Imaging Tasks.\u003c\/p\u003e \u003cp\u003e1.3 Examples of Optical Imaging.\u003c\/p\u003e \u003cp\u003e1.4 ImagingTasks inMedical Imaging.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Operators and Functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Classes of Imaging Operators.\u003c\/p\u003e \u003cp\u003e2.2 Continuous and Discrete Functions.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Vectors with Real-Valued Components.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Scalar Products.\u003c\/p\u003e \u003cp\u003e3.2 Matrices.\u003c\/p\u003e \u003cp\u003e3.3 Vector Spaces.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Complex Numbers and Functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Arithmetic of Complex Numbers.\u003c\/p\u003e \u003cp\u003e4.2 Graphical Representation of Complex Numbers.\u003c\/p\u003e \u003cp\u003e4.3 Complex Functions.\u003c\/p\u003e \u003cp\u003e4.4 Generalized Spatial Frequency – Negative Frequencies.\u003c\/p\u003e \u003cp\u003e4.5 Argand Diagrams of Complex-Valued Functions.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Complex-Valued Matrices and Systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Vectors with Complex-Valued Components.\u003c\/p\u003e \u003cp\u003e5.2 Matrix Analogues of Shift-Invariant Systems.\u003c\/p\u003e \u003cp\u003e5.3 Matrix Formulation of ImagingTasks.\u003c\/p\u003e \u003cp\u003e5.4 Continuous Analogues of Vector Operations.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 1-D Special Functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Definitions of 1-D Special Functions.\u003c\/p\u003e \u003cp\u003e6.2 1-D Dirac Delta Function.\u003c\/p\u003e \u003cp\u003e6.3 1-D Complex-Valued Special Functions.\u003c\/p\u003e \u003cp\u003e6.4 1-D Stochastic Functions–Noise.\u003c\/p\u003e \u003cp\u003e6.5 Appendix A: Area of \u003ci\u003eSINC\u003c\/i\u003e[\u003ci\u003ex\u003c\/i\u003e] and \u003ci\u003eSINC\u003c\/i\u003e2[\u003ci\u003ex\u003c\/i\u003e].\u003c\/p\u003e \u003cp\u003e6.6 Appendix B: Series Solutions for Bessel Functions \u003ci\u003eJ\u003c\/i\u003e0[\u003ci\u003ex\u003c\/i\u003e] and \u003ci\u003eJ\u003c\/i\u003e1[\u003ci\u003ex\u003c\/i\u003e].\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 2-D Special Functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 2-D Separable Functions.\u003c\/p\u003e \u003cp\u003e7.2 Definitions of 2-D Special Functions.\u003c\/p\u003e \u003cp\u003e7.3 2-D Dirac Delta Function and its Relatives.\u003c\/p\u003e \u003cp\u003e7.4 2-D Functions with Circular Symmetry.\u003c\/p\u003e \u003cp\u003e7.5 Complex-Valued 2-D Functions.\u003c\/p\u003e \u003cp\u003e7.6 Special Functions of Three (orMore) Variables.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Linear Operators.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Linear Operators.\u003c\/p\u003e \u003cp\u003e8.2 Shift-Invariant.Operators.\u003c\/p\u003e \u003cp\u003e8.3 Linear Shift-Invariant (LSI) Operators.\u003c\/p\u003e \u003cp\u003e8.4 Calculating Convolutions.\u003c\/p\u003e \u003cp\u003e8.5 Properties of Convolutions.\u003c\/p\u003e \u003cp\u003e8.6 Autocorrelation.\u003c\/p\u003e \u003cp\u003e8.7 Crosscorrelation.\u003c\/p\u003e \u003cp\u003e8.8 2-DLSIOperations.\u003c\/p\u003e \u003cp\u003e8.9 Crosscorrelations of 2-D Functions.\u003c\/p\u003e \u003cp\u003e8.10 Autocorrelations of 2-D.Functions.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Fourier Transforms of 1-D Functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Transforms of Continuous-Domain Functions.\u003c\/p\u003e \u003cp\u003e9.2 Linear Combinations of Reference Functions.\u003c\/p\u003e \u003cp\u003e9.3 Complex-Valued Reference Functions.\u003c\/p\u003e \u003cp\u003e9.4 Transforms of Complex-Valued Functions.\u003c\/p\u003e \u003cp\u003e9.5 Fourier Analysis of Dirac Delta Functions.\u003c\/p\u003e \u003cp\u003e9.6 Inverse Fourier Transform.\u003c\/p\u003e \u003cp\u003e9.7 Fourier Transforms of 1-D Special Functions.\u003c\/p\u003e \u003cp\u003e9.8 Theorems of the Fourier Transform.\u003c\/p\u003e \u003cp\u003e9.9 Appendix: Spectrum of Gaussian via Path Integral.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Multidimensional Fourier Transforms.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 2-D Fourier Transforms.\u003c\/p\u003e \u003cp\u003e10.2 Spectra of Separable 2-D Functions.\u003c\/p\u003e \u003cp\u003e10.3 Theorems of 2-D Fourier Transforms.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Spectra of Circular Functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Hankel Transform.\u003c\/p\u003e \u003cp\u003e11.2 Inverse Hankel Transform.\u003c\/p\u003e \u003cp\u003e11.3 Theorems of Hankel Transforms.\u003c\/p\u003e \u003cp\u003e11.4 Hankel Transforms of Special Functions.\u003c\/p\u003e \u003cp\u003e11.5 Appendix: Derivations of Equations (11.12) and (11.14).\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 The Radon Transform.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Line-Integral Projections onto Radial Axes.\u003c\/p\u003e \u003cp\u003e12.2 Radon Transforms of Special Functions.\u003c\/p\u003e \u003cp\u003e12.3 Theorems of the Radon Transform.\u003c\/p\u003e \u003cp\u003e12.4 Inverse Radon Transform.\u003c\/p\u003e \u003cp\u003e12.5 Central-Slice Transform.\u003c\/p\u003e \u003cp\u003e12.6 Three Transforms of Four Functions.\u003c\/p\u003e \u003cp\u003e12.7 Fourier and Radon Transforms of Images.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Approximations to Fourier Transforms.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Moment Theorem.\u003c\/p\u003e \u003cp\u003e13.2 1-D Spectra via Method of Stationary Phase.\u003c\/p\u003e \u003cp\u003e13.3 Central-Limit Theorem.\u003c\/p\u003e \u003cp\u003e13.4 Width Metrics and Uncertainty Relations.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Discrete Systems, Sampling, and Quantization.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Ideal Sampling.\u003c\/p\u003e \u003cp\u003e14.2 Ideal Sampling of Special Functions.\u003c\/p\u003e \u003cp\u003e14.3 Interpolation of Sampled Functions.\u003c\/p\u003e \u003cp\u003e14.4 Whittaker–Shannon Sampling Theorem.\u003c\/p\u003e \u003cp\u003e14.5 Aliasingand Interpolation.\u003c\/p\u003e \u003cp\u003e14.6 “Prefiltering” to Prevent Aliasing.\u003c\/p\u003e \u003cp\u003e14.7 Realistic Sampling.\u003c\/p\u003e \u003cp\u003e14.8 Realistic Interpolation.\u003c\/p\u003e \u003cp\u003e14.9 Quantization.\u003c\/p\u003e \u003cp\u003e14.10 Discrete Convolution.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Discrete Fourier Transforms.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Inverse of the Infinite-Support DFT.\u003c\/p\u003e \u003cp\u003e15.2 DFT over Finite Interval.\u003c\/p\u003e \u003cp\u003e15.3 Fourier Series Derived from Fourier Transform.\u003c\/p\u003e \u003cp\u003e15.4 Efficient Evaluation of the Finite DFT. \u003c\/p\u003e \u003cp\u003e15.5 Practical Considerations for DFT and FFT.\u003c\/p\u003e \u003cp\u003e15.6 FFTs of 2-D Arrays.\u003c\/p\u003e \u003cp\u003e15.7 Discrete Cosine Transform.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Magnitude Filtering.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Classes of Filters.\u003c\/p\u003e \u003cp\u003e16.2 Eigenfunctions of Convolution.\u003c\/p\u003e \u003cp\u003e16.3 Power Transmission of Filters.\u003c\/p\u003e \u003cp\u003e16.4 Lowpass Filters.\u003c\/p\u003e \u003cp\u003e16.5 Highpass Filters.\u003c\/p\u003e \u003cp\u003e16.6 Bandpass Filters.\u003c\/p\u003e \u003cp\u003e16.7 Fourier Transform as a Bandpass Filter.\u003c\/p\u003e \u003cp\u003e16.8 Bandboost and Bandstop Filters.\u003c\/p\u003e \u003cp\u003e16.9 Wavelet Transform.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Allpass (Phase) Filters.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Power-Series Expansion for Allpass Filters.\u003c\/p\u003e \u003cp\u003e17.2 Constant-Phase Allpass Filter.\u003c\/p\u003e \u003cp\u003e17.3 Linear-Phase Allpass Filter.\u003c\/p\u003e \u003cp\u003e17.4 Quadratic-Phase Filter.\u003c\/p\u003e \u003cp\u003e17.5 Allpass Filters with Higher-Order Phase.\u003c\/p\u003e \u003cp\u003e17.6 Allpass Random-Phase Filter.\u003c\/p\u003e \u003cp\u003e17.7 Relative Importance of Magnitude and Phase.\u003c\/p\u003e \u003cp\u003e17.8 Imaging of Phase Objects.\u003c\/p\u003e \u003cp\u003e17.9 Chirp Fourier Transform.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Magnitude–Phase Filters.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Transfer Functions of Three Operations.\u003c\/p\u003e \u003cp\u003e18.2 Fourier Transform of Ramp Function.\u003c\/p\u003e \u003cp\u003e18.3 Causal Filters.\u003c\/p\u003e \u003cp\u003e18.4 Damped Harmonic Oscillator.\u003c\/p\u003e \u003cp\u003e18.5 Mixed Filters with Linear or Random Phase.\u003c\/p\u003e \u003cp\u003e18.6 Mixed Filter with Quadratic Phase.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Applications of Linear Filters.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Linear Filters for the Imaging Tasks.\u003c\/p\u003e \u003cp\u003e19.2 Deconvolution– “Inverse Filtering”.\u003c\/p\u003e \u003cp\u003e19.3 Optimum Estimators for Signals in Noise.\u003c\/p\u003e \u003cp\u003e19.4 Detection of Known Signals – Matched Filter.\u003c\/p\u003e \u003cp\u003e19.5 Analogies of Inverse and Matched Filters.\u003c\/p\u003e \u003cp\u003e19.6 Approximations to Reciprocal Filters.\u003c\/p\u003e \u003cp\u003e19.7 Inverse Filtering of Shift-Variant Blur.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Filtering in Discrete Systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Translation, Leakage, and Interpolation.\u003c\/p\u003e \u003cp\u003e20.2 Averaging Operators– Lowpass Filters.\u003c\/p\u003e \u003cp\u003e20.3 Differencing Operators – Highpass Filters.\u003c\/p\u003e \u003cp\u003e20.4 Discrete Sharpening Operators.\u003c\/p\u003e \u003cp\u003e20.5 2-DGradient.\u003c\/p\u003e \u003cp\u003e20.6 Pattern Matching.\u003c\/p\u003e \u003cp\u003e20.7 Approximate Discrete Reciprocal Filters.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Optical Imaging in Monochromatic Light.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Imaging Systems Based on Ray Optics Model.\u003c\/p\u003e \u003cp\u003e21.2 Mathematical Model of Light Propagation.\u003c\/p\u003e \u003cp\u003e21.3 Fraunhofer Diffraction.\u003c\/p\u003e \u003cp\u003e21.4 Imaging System based on Fraunhofer Diffraction.\u003c\/p\u003e \u003cp\u003e21.5 Transmissive Optical Elements.\u003c\/p\u003e \u003cp\u003e21.6 Monochromatic Optical Systems.\u003c\/p\u003e \u003cp\u003e21.7 Shift-Variant Imaging Systems.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Incoherent Optical Imaging Systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Coherence.\u003c\/p\u003e \u003cp\u003e22.2 Polychromatic Source – Temporal Coherence.\u003c\/p\u003e \u003cp\u003e22.3 Imaging in Incoherent Light.\u003c\/p\u003e \u003cp\u003e22.4 System Function in Incoherent Light.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Holography.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Fraunhofer Holography.\u003c\/p\u003e \u003cp\u003e23.2 Holography in Fresnel Diffraction Region.\u003c\/p\u003e \u003cp\u003e23.3 Computer-Generated Holography.\u003c\/p\u003e \u003cp\u003e23.4 Matched Filtering with Cell-Type CGH.\u003c\/p\u003e \u003cp\u003e23.5 Synthetic-Aperture Radar (SAR).\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex.\u003c\/b\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Electronics \u0026amp; communications engineering [\u003ca title=\"See our other books on Electronics \u0026amp; communications engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Electronics%20\u0026amp;%20communications%20engineering%20%5BTJ%5D%22\"\u003eTJ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52278021751064,"sku":"9780470689837","price":106.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470689837.jpg?v=1781455815","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/fourier-methods-in-imaging-hardback-9780470689837","provider":"Freshly Printed Books","version":"1.0","type":"link"}