Fourier Methods in Imaging
Wiley-IS&T Series in Imaging Science and Technology
2. Auflage Mai 2010
954 Seiten, Hardcover
Wiley & Sons Ltd
Kurzbeschreibung
Fourier Methods in Imaging first introduces the basic mathematical concepts of linear algebra for vectors and functions, a knowledge of which is necessary for understanding the subsequent discussions. The second section lays out the mathematical operations and transformations of continuous functions that are useful for describing imaging systems. 'Special' functions, such as the Fourier transforms of 1-D and 2-D functions, and the Radon transform, are looked at in detail. Most applications act on discrete functions and these (through the Fourier transform) are discussed in the important third section. The fourth section discusses the description of imaging systems as linear 'filters' and applies the mathematical tools to solve specific imaging tasks.
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
Preface
1 Introduction
2 Operators and Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Vectors with Real-Valued Components
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Complex Numbers and Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Complex-Valued Matrices and Systems
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 1-D Special Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 2-D Special Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Linear Operators
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 Fourier Transforms of 1-D Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 Multidimensional Fourier Transforms
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11 Spectra of Circular Functions
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12 The Radon Transform
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13 Approximations to Fourier Transforms 13.1 Moment Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14 Discrete Systems, Sampling, and Quantization
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15 Discrete Fourier Transforms 511
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16 Magnitude Filtering
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17 Allpass (Phase) Filters
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18 Magnitude-Phase Filters
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19 Applications of Linear Filters
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20 Filtering in Discrete Systems
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21 Optical Imaging in Monochromatic Light
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22 Incoherent Optical Imaging Systems
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23 Holography
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References
Index