2. Edition - May 2010
129.- Euro
2010. 954 Pages, Hardcover
ISBN-10: 0-470-68983-8
ISBN-13: 978-0-470-68983-7 - John Wiley & Sons






Sample Chapter

Short description
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.

From the contents
Series Editor's Preface

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