The fractional Fourier transform and its application to high resolution SAR imaging
The fractional Fourier transform and its application to high resolution SAR imaging
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分数阶傅里叶变换及其在高分辨率SAR成像中的应用
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
J. Soraghan
中科院分区：
文献类型：
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作者：
A. Amein;J. Soraghan
分数阶傅里叶变换（FrFT）是傅里叶变换的一种推广形式，它开辟了一系列新的应用领域，包括雷达、模式识别和合成孔径雷达（SAR）图像处理等。Chirp Scaling算法（CSA）是一种重要的雷达成像算法。它是有吸引力的，因为它出色的聚焦能力和实现简单。利用分数阶傅里叶变换（FrFT）在非平稳信号处理和分析中的固有结构，提出了一种新的基于分数阶傅里叶变换（FrFT）的CSA。引入的分数阶线性调频标度算法（FrCSA）在方位角方向上应用快速傅立叶变换（FFT）而不是分数阶傅立叶变换（FrFT），仅用于分析开发易处理性目的，因为它在两个维度上都是数值易处理的。为了证明使用FrCSA在方位维度上的分辨率和聚焦增强，并且还能够执行方位分数滤波、噪声去除和飞行路径非线性补偿，需要方位分数变换的闭合形式表达式。在这次演讲中，我们提出了一个封闭的形式表达的方位分数傅里叶变换的新的FrCSA应用于高分辨率成像的数学推导。使用分数线性调频缩放算法或任何其他线性调频型SAR成像算法中基于FrFT的方位角表达式而不是经典的基于FFT的方位角表达式，真实的SAR数据图像的结果将显示出显着增强的特征。
The fractional Fourier transform (FrFT), which is a generalized form of the well-known Fourier transform, has opened up the possibility of a new range of potentially promising and useful applications including radar involving the use and detection of chirp signals, pattern recognition and Synthetic Aperture Radar (SAR) image processing. The Chirp Scaling Algorithm (CSA) is one of the most important and well-known radar imaging algorithms. It is attractive because of its excellent focusing ability and implementation simplicity. Benefiting from the inherent structure of the FrFT for non- stationary digital signal processing and analysis, especially for chirped-type signals, a new version of the CSA based on the Fractional Fourier Transform (FrFT) is developed. The introduced Fractional Chirp Scaling Algorithm (FrCSA) applied the Fast Fourier Transform (FFT) instead of the fractional Fourier transform (FrFT) in the azimuth direction for the analytical development tractability purposes only as it numerically tractable in both dimensions. To demonstrate the resolution and focusing enhancement in the azimuth dimension using the FrCSA and also to be able to perform azimuth fractional filtering, noise removal and flight path nonlinearity compensation, a closed form expression for the azimuth fractional transformation is required. In this talk we present the mathematical derivation for a closed- form expression of the azimuth-fractional Fourier transform of the new FrCSA with application to high resolution imaging. Results to real SAR data images will show significantly enhanced features using the FrFT-based azimuth expression instead of the classical FFT-based one within the fractional chirp scaling algorithm or any other chirped-type SAR imaging algorithm.