MATLAB算法实现逆合成孔径雷达成像详解

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"《利用MATLAB算法进行逆合成孔径雷达成像》是一本由CANERÖZDEMI博士撰写的专业书籍，发表于2012年，由John Wiley & Sons, Inc.出版。该书聚焦于将逆合成孔径雷达（InSAR）技术与MATLAB编程语言相结合，为读者提供了深入理解和应用这一复杂成像技术的实用指导。逆合成孔径雷达是一种利用信号处理技术对地球表面进行高分辨率遥感的技术。通过模拟合成一个大孔径雷达系统的操作，即使在有限的天线移动范围内，也能生成高精度的图像。MATLAB作为一款强大的数值计算软件，因其易用性和灵活性在科学计算、数据分析等领域广泛应用，将它与InSAR算法结合，有助于简化复杂的信号处理流程，提高图像重建的效率和准确性。本书涵盖了以下几个关键知识点： 1. 理论基础：首先，作者会介绍InSAR的工作原理，包括多普勒效应、干涉测量原理和相位解缠绕等核心概念，确保读者对基本理论有深刻理解。 2. MATLAB工具箱：详细讲解如何利用MATLAB的信号处理工具箱，如Signal Processing Toolbox和Image Processing Toolbox，实现数据采集、预处理、相位解缠绕、干涉图生成以及后处理等步骤。 3. 实例分析：书中提供了一系列实际案例，展示了如何使用MATLAB代码解决实际的InSAR问题，如地形测绘、城市变化检测和自然灾害监测等，使读者能够通过实践加深理解。 4. 算法优化与高级技术：探讨了如何利用MATLAB的优化功能和高级特性，如并行计算、自定义函数和深度学习方法，来改进InSAR成像的性能和效率。 5. 最新进展和挑战：书中还关注了当前InSAR领域的研究动态和未来发展趋势，讨论了在MATLAB环境下可能面临的挑战以及如何应对这些挑战。《利用MATLAB算法进行逆合成孔径雷达成像》是一本实用的指南，不仅适合从事遥感和信号处理的科研人员，也适用于希望学习并应用InSAR技术的工程师和学生。通过阅读这本书，读者不仅能掌握MATLAB在InSAR中的具体应用，还能提升其在该领域的专业技能。"

CHAPTER ONE

Basics of Fourier Analysis

1.1 FORWARD AND INVERSE FOURIER TRANSFORM

Fourier transform (FT) is a common and useful mathematical tool that is

utilized in numerous applications in science and technology. FT is quite practi-

cal, especially for characterizing nonlinear functions in nonlinear systems,

analyzing random signals, and solving linear problems. FT is also a very impor-

tant tool in radar imaging applications as we shall investigate in the forthcom-

ing chapters of this book. Before starting to deal with the FT and inverse

Fourier transform (IFT), a brief history of this useful linear operator and its

founders is presented.

1.1.1 Brief History of FT

Jean Baptiste Joseph Fourier, a great mathematician, was born in 1768 in

Auxerre, France. His special interest in heat conduction led him to describe a

mathematical series of sine and cosine terms that can be used to analyze

propagation and diffusion of heat in solid bodies. In 1807, he tried to share his

innovative ideas with researchers by preparing an essay entitled “On the

Propagation of Heat in Solid Bodies.” The work was examined by Lagrange,

Laplace, Monge, and Lacroix. Lagrange’s oppositions caused the rejection of

Fourier’s paper. This unfortunate decision caused colleagues to wait for 15

more years to read his remarkable contributions on mathematics, physics, and,

especially, signal analysis. Finally, his ideas were published in the book The

Analytic Theory of Heat in 1822 [1].

Discrete Fourier transform (DFT) was developed as an effective tool in

calculating this transformation. However, computing FT with this tool in the

Inverse Synthetic Aperture Radar Imaging with MATLAB Algorithms, First Edition.

Caner Özdemir.

2 Basics of fourier analysis

19th century was taking a long time. In 1903, Carl Runge studied the minimiza-

tion of the computational time of the transformation operation [2]. In 1942,

Danielson and Lanczos utilized the symmetry properties of FT to reduce the

number of operations in DFT [3]. Before the advent of digital computing

technologies, James W. Cooley and John W. Tukey developed a fast method

to reduce the computation time in DFT. In 1965, they published their technique

that later on became famous as the fast Fourier transform (FFT) [4].

1.1.2 Forward FT Operation

The FT can be simply deﬁned as a certain linear operator that maps functions

or signals deﬁned in one domain to other functions or signals in another

domain. The common use of FT in electrical engineering is to transform signals

from time domain to frequency domain or vice versa. More precisely, forward

FT decomposes a signal into a continuous spectrum of its frequency compo-

nents such that the time signal is transformed to a frequency-domain signal.

In radar applications, these two opposing domains are usually represented as

“spatial frequency” (or wave number) and “range” (distance). Such use of FT

will be examined and applied throughout this book.

The forward FT of a continuous signal g(t) where −∞ < t < ∞ is described

G f g t

g t e dt

j ft

( )

{ }

( )

⋅

−

−∞

∞

∫

ℱ

(1.1)

To appreciate the meaning of FT, the multiplying function e

−j2πft

and operators

(multiplication and integration) on the right side of Equation 1.1 should be

investigated carefully: The term

j f t

− 2

is a complex phasor representation for

a sinusoidal function with the single frequency of f

. This signal oscillates only

at the frequency of f

and does not contain any other frequency component.

Multiplying the signal in interest, g(t), with the term

j f t

−

provides the simi-

larity between each signal, that is, how much of g(t) has the frequency content

of f

. Integrating this multiplication over all time instances from −∞ to ∞ will

sum the f

contents of g(t) over all time instants to give G(f

); that is, the

amplitude of the signal at the particular frequency of f

. Repeating this process

for all the frequencies from −∞ to ∞ will provide the frequency spectrum of

the signal; that is, G( f ) . Therefore, the transformed signal represents the

continuous spectrum of frequency components; that is, representation of the

signal in “frequency domain.”

1.1.3 IFT

This transformation is the inverse operation of the FT. IFT, therefore, synthe-

sizes a frequency-domain signal from its spectrum of frequency components

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