## 2 Enhancement Methods for High-Resolution SAR Ship Wake Processing
### Ship Wake Enhancement Method Based on Equivalent Sequence Images  
Many scholars at home and abroad have studied the method of dividing the single-channel azimuth into sub-apertures to effectively obtain signals in the range-Doppler domain for two or more channels. They utilize multi-channel techniques, such as adaptive time integration (ATI), displaced phase center antenna (DPCA), and space-time adaptive processing (STAP) to suppress stationary clutter and detect moving targets [25]. Inspired by the enhancement and detection methods for stable point targets in single-channel multi-apertures, a ship wake enhancement method based on overlap sub-aperture magnitude images (OSMI) in the azimuth overlap sub-aperture amplitude image sequence is proposed. This method enhances the linear features of wakes in the imaging process to obtain high-quality original images, laying the foundation for subsequent wake detection applications. The following Figure 3 depicts the flowchart of the wake enhancement algorithm. Figure 3: Flowchart for the equivalent sequence image wake enhancement method. The method includes the following steps: (1) The proposed method begins with inputting a single-look complex (SLC) image, which is then sliced to generate a sequence of sub-aperture images. (2) These sub-aperture images undergo standard deviation and mean equalization processing to ensure that the grayscale values of the equalized images have the same standard deviation and variance. (3) The equalized images are subjected to median filtering to remove noise. (4) The wake-enhanced image is outputted. According to Equation (1), during the synthetic aperture time in SAR imaging, ground targets are continuously illuminated, and the azimuth signal exhibits linear frequency modulation characteristics. Therefore, using the correspondence between the azimuth signal spectrum and the azimuth angle, sub-aperture slicing can be achieved in the azimuth frequency domain. By separately imaging each sub-aperture data, equivalent timeseries images can be obtained. Let the azimuth signal bandwidth be \(B\), and the number of sequence images be \(N\). Hence, each sub-image has a bandwidth of \(B/N\) in the azimuth direction to obtain overlapping sub-images and maintain a certain bandwidth overlap for each sub-aperture image. During the processing, a fixed sliding window is used to ensure the same resolution and overlap requirements. During the implementation process, the SLC sub-apertures are processed one by one. FFT transformation is performed along the azimuth direction of SLC data, and a fixed sliding window is used to segment the frequency spectrum of the azimuth signal, obtaining \(N\) segments corresponding to different azimuth angles. The segmented echo signals in the range-Doppler domain are subjected to inverse Fourier transform in the azimuth direction to obtain timeseries sub-aperture SAR images, which are indexed based on the azimuth perspective of each sub-aperture image. Before enhancing the linear features, it is necessary to standardize and equalize the sub-sequence images. This is achieved by intensity normalization to achieve relative histogram equalization. Due to the scattering characteristics of the sea surface, the grayscale values of pixels on the sea surface are correlated with the azimuth imaging angle, requiring the elimination of intensity differences caused by antenna pointing and directional patterns. Firstly, the histogram distribution of all sub-sequence images is calculated, and the mean \(\mu_{i}\) and standard deviation \(\sigma_{i}\) of each image are computed. Histogram intensity normalization is then applied to each image in the OSMI, equalizing the grayscale values based on the mean and standard deviation, ensuring uniformity in terms of standard values and variance across all sub-images.