## 2 Enhancement Methods for High-Resolution SAR Ship Wake Processing
### High-Resolution Spaceborne SAR Wake Imaging  
As a typical model of random rough surface scattering, ocean waves exhibit dynamic characteristics due to their complex motion. In SAR imaging, there exists Bragg resonance between the ocean waves and SAR electromagnetic waves. Under moderate incidence angle conditions, certain frequencies of incident electromagnetic waves and waves in the ocean will emit coherent superimposed enhanced echoes, forming Bragg resonance. Therefore, the actual wake structure obtained in imaging exhibits complex phenomena and is influenced by various factors, such as ocean environmental parameters, vessel motion parameters, or radar parameters and imaging processing algorithms. High-resolution spaceborne SAR adopts sliding spotlight mode for imaging. In the sliding spotlight mode, the antenna does not point to a fixed area within the illuminated scene but instead points to a virtual rotation center below the illuminated plane (rotation  
Figure 1: Typical ship wake image in spaceborne SAR. center), as shown in Figure 2. The ground projection of the antenna beam essentially slides along the direction of satellite flight within the illuminated scene, as illustrated in the figure below. Therefore, the synthetic aperture time of sliding spotlight SAR is relatively long, reaching the order of seconds or even tens of seconds. This prolonged synthetic aperture time in sliding spotlight mode allows for the collection of more comprehensive information, especially regarding moving targets, such as ships and their wakes, resulting in improved imaging quality and wake detection capabilities. According to the spatial geometry model of spaceborne SAR, the SAR imaging processing can be viewed as a two-dimensional correlation process to extract the target area's scattering coefficient using the acquired echo data, which includes range compensation processing and azimuth compensation processing:  
1. Range Compensation Processing: This is a one-dimensional shift-invariant process with a known correlation kernel. It compensates for the effects of range migration and focuses the radar signal in the range direction. 2. Azimuth Compensation Processing: Due to the presence of range migration, azimuth compensation processing involves a two-dimensional time-variant correlation process. It compensates for the effects of Doppler shifts caused by the relative motion between the radar platform and the target scene. Linear chirp scaling and other imaging algorithms are commonly used in SAR processing. After range compression and compensation for various azimuth error factors, the echo signals \(ss\) in the SAR image's range-Doppler domain are obtained. Typically, matched filtering is used for azimuth focusing processing. After azimuth Fourier inverse transformation, ignoring the complex constant, the original SAR image is obtained [22]. \[ \begin{split} ss(\tau,f_{a})&=\sigma(t)\cdot W_{ac} (t)\cdot A\Big{(}\tau-\frac{2\tau\sin\varphi}{\varsigma\sin\varphi_{\tau\tau}} \Big{)}\\ &\cdot\exp\left\{-\mathrm{i}\frac{4\pi\tau}{\lambda}t\sin\varphi \sqrt{1-\left(\frac{\lambda f_{a}}{2\varphi}\right)^{2}}\right\}\,\end{split}  \tag{1}\]  
In the equations:  
* \(\sigma(t)\) represents the backscattering coefficient of the sea surface, which varies with the azimuthal imaging angle. * \(W_{ac}(\cdot)\) represents the envelope after azimuth antenna transformation. Figure 2: Sliding spotlight SAR imaging (The dotted lines indicate the target is illuminated). * \(A(\cdot)\) represents the envelope after linear frequency modulation compression processing in the range direction. * \(\phi\) represents the effective slant angle. * \(\phi_{ref}\) represents the reference effective slant angle. * \(r\) represents the slant range at the moment of beam center when using the equivalent slant range model. * \(f_{a}\) represents the azimuth frequency. * \(v\) represents the effective velocity.