Fundamentals of Bistatic SAR Imaging Algorithms
The formulation of a point target spectrum in synthetic aperture radar (SAR) is a key step in SAR focusing algorithms, which exploits the processing efficiency in the frequency domain. The general bistatic SAR range equation has a double-square-root (DSR)
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Fundamentals of Bistatic SAR Imaging Algorithms
Abstract The formulation of a point target spectrum in synthetic aperture radar (SAR) is a key step in SAR focusing algorithms, which exploits the processing efficiency in the frequency domain. The general bistatic SAR range equation has a double-square-root (DSR) term that makes it difficult to derive an analytical expression of the bistatic two-dimensional spectrum. Many researchers overcome this difficulty by developing an approximation of the two-dimensional bistatic point target reference spectrum (BPTRS) and using the result to develop efficient frequency domain focusing algorithms for bistatic SAR data. In this chapter, three BPTR spectra are discussed and derived in detail. These consist of the Loffeld bistatic formula (LBF), the extended Loffeld bistatic formula (ELBF), and the method of series reversion (MSR). These three formulations are based on the principle of stationary phase (POSP).
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Introduction
For bistatic SAR focusing, time-domain methods can be used to focus echo signals for any acquisition scenario with any arbitrary flight trajectories without approximation error [1]. These methods are used to produce computerized tomography in medical imaging and geophysical tomography in geophysical imaging. However, these methods incur heavy computational cost that scales with an order of OðN 3 Þ, where N 2 is the number of pixels in the image [1]. By substituting the time-consuming superposition integrals in the space-time domain by fast convolution in the frequency domain, the processing efficiency can be greatly improved. For the monostatic case, an analytical solution exists for the point target spectrum [2]. Many efficient monostatic algorithms [2] are developed based on this analytical monostatic point target spectrum. These frequency-domain algorithms achieve a computational cost that scales on the order of OðN 2 log2 N Þ. Deriving the point target spectrum is basically an inversion problem that must be solved to arrive at a frequency representation of the time domain signal history of the point target trajectory. For the bistatic case, there is no analytical solution for the © Springer Nature Singapore Pte Ltd. 2018 R. Wang and Y. Deng, Bistatic SAR System and Signal Processing Technology, https://doi.org/10.1007/978-981-10-3078-9_2
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2 Fundamentals of Bistatic SAR Imaging Algorithms
point target spectrum due to the double-square-root (DSR) function in the range equation. This bistatic range history has the form of a flat-top hyperbola [3]. As there is no analytical solution for the BPTRS, it can only be determined approximately or numerically. Several approximate bistatic point target reference spectra and bistatic imaging methods have been derived based on these approximate analytical spectra. In this section, three generic approaches are discussed. The first method transforms the bistatic data to a monostatic equivalent as a preprocessing step. After this preprocessing step, the data can be focused by a monostatic focusing algorithm. In [4
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