WakeGAN: Domain Adaptation for SAR Wakes

• WakeGAN is a structure-preserving GAN for style transfer that rigorously maintains wake geometry while bridging optical and SAR domains.
• It employs dedicated spectral and spatial modules like the Frequency Selection Unit and Detail Enhancement Guide to decompose and enhance image features.
• WakeGAN achieves significant performance gains in SAR wake detection by enforcing dual spectral losses and instance-level feature filtering.

WakeGAN is a structure-preserving generative adversarial network designed for style transfer between domains in ship wake detection, with primary application in bridging the complex gap between annotated optical images and noisy synthetic aperture radar (SAR) imagery. Within the SimMemDA framework, WakeGAN is responsible for transforming optical images into pseudo-SAR images, reducing low-level appearance differences while rigorously maintaining the geometric integrity of wake features. This approach addresses fundamental challenges in unsupervised domain adaptation for SAR-based wake detection, where optical images possess clearer annotations and SAR images are abstract and difficult to label.

1. Structure-Preserving Style Transfer Architecture

WakeGAN differs from generic image-to-image translation models through its targeted preservation of wake-specific geometries and textures. The generator network is architected with dedicated spectral and spatial modules:

• Frequency Selection Unit (FSU): Shallow features $F_s$ are decomposed into low-frequency $F_l$ and high-frequency $F_h$ components. The decomposition utilizes learned depthwise convolutional filters $W_{\mathrm{LP}}^{(i)}$ and softmax normalization, specifically:

$F_l^{(i)} = W_{\mathrm{LP}}^{(i)} * F_s^{(i)},$

$$F_h^{(i)} = (I_k^{(i)} - W_{\mathrm{LP}}^{(i)}) * F_s^{(i)}.$$

This explicit separation aids in capturing both wake geometry (low-frequency signal) and fine SAR scattering patterns (high-frequency details).

• Detail Enhancement Guide (DEG): The DEG operates on high-frequency branches and uses modulatory guidance via a learnable template $W_h$. Deformable window attention mechanisms further enhance detail retention:

$$O_h = \tilde{V}_h \cdot \operatorname{Softmax}\left( \frac{Q_h \cdot \tilde{K}_h^{\top}}{\sqrt{d}} \right),$$

where keys and values are dynamically corrected by offsets derived from $Q_h$, reinforcing texture and edge cues fundamental to SAR imagery.

• Structure Preserving Guide (SPG): Low-frequency features undergo Fourier transformation, block-wise mixing, and soft-thresholding. The multi-token cross-attention mechanism then enforces geometry preservation; spectral features $\hat{F}_l = \mathcal{F}(\tilde{F}_l)$ are monitored so that the final output after inverse transformation maintains input wake geometry.

2. Dual Spectral Losses and Feature Consistency

WakeGAN employs two loss functions that jointly constrain both spectral and textural fidelity:

• Spectral Preservation Loss (SPL):

$$\mathcal{L}_{\mathrm{SPL}}(G_\mathcal{S}, x^S) = \mathbb{E}_{x^S \sim \mathcal{S}} \Bigl[ \| p_L(x^S) - p_L(G_\mathcal{S}(x^S)) \|_2^2 + \lambda_H d_H(p_H(x^S), p_H(G_\mathcal{S}(x^S))) \Bigr],$$

where $p_L(\cdot)$ and $p_H(\cdot)$ extract, respectively, low- and high-frequency bands and $d_H(\cdot,\cdot)$ is a directional cosine distance metric over high-frequency features.

• Cyclic Spectral Consistency Loss (CSCL):

$$\begin{aligned} &\mathcal{L}_{\mathrm{CSCL}}(G_\mathcal{S}, G_\mathcal{T}) = \mathbb{E}_{x^S \sim \mathcal{S}} \Bigl[ \| p_L(x^S) - p_L(\bar{x}^S) \|_2^2 + \lambda_H d_H(p_H(x^S), p_H(\bar{x}^S)) \Bigr] \ & + \mathbb{E}_{x^T \sim \mathcal{T}} \Bigl[ \| p_L(x^T) - p_L(\bar{x}^T) \|_2^2 + \lambda_H d_H(p_H(x^T), p_H(\bar{x}^T)) \Bigr], \end{aligned}$$

with $\bar{x}^S = G_\mathcal{T}(G_\mathcal{S}(x^S))$. This cyclic loss enforces that mappings in both directions (optical to pseudo-SAR and back) are spectrally and structurally consistent.

3. Instance-Level Feature Similarity Filtering

To minimize negative transfer, SimMemDA incorporates a filtering process following WakeGAN’s translation. Each pseudo-SAR instance’s feature embedding $\phi_i^s$ is compared to parameterized distributions over real SAR features $\Theta(\theta_t)$. Methods include:

• Prototype (mean) filtering:

$$\theta_t = \frac{1}{|\Phi_t|} \sum_{j=1}^{|\Phi_t|} \phi_j^t, \quad d_i^s = \| \phi_i^s - \theta_t \|^2$$

• Gaussian Mixture filtering:

$$d_i^s = \frac{1}{\sum_{m=1}^M \alpha_m \mathcal{N}(\phi_i^s; \mu_m, \Sigma_m)}$$

Instances with smallest $d_i^s$—i.e., those most similar to the target SAR domain—are selected for subsequent training, sharply reducing the risk of domain mismatch and improving sample relevance.

4. Memory-Guided Pseudo-Label Calibration

Unlabeled SAR detection relies on pseudo-labels, which are susceptible to noise. WakeGAN enables dependable pseudo-labeling via:

• Feature-Confidence Memory Bank: Feature embeddings and their confidences are stored across training, updated by

$\theta_t' \leftarrow m \theta_t' + (1-m) \theta_t$

preserving evolving domain characteristics.

• K-nearest neighbor confidence fusion: Cosine similarities $\{\alpha_i\}$ serve as weights

$$w_i = \frac{\exp(\gamma \alpha_i)}{\sum_j \exp(\gamma \alpha_j)},$$

for fusing confidences across $K$ nearest memory features:

$c_{\text{neighbor}} = \sum_{i=1}^K w_i c_i$

and final confidence blending

$c_f = \delta c_z + (1-\delta) c_{\text{neighbor}}$

further calibrated by geometric priors (e.g., wake linearity) and adaptive thresholding. This strategy robustifies the selection of high-quality pseudo-labels for continued network training.

5. Experimental Evaluation and Empirical Impact

SimMemDA, with WakeGAN as its initial style transfer stage, demonstrates marked improvement in cross-modal SAR wake detection. Quantitative metrics illustrate:

Configuration	[email protected]	[email protected]:0.05:0.95
Source Only (Style Transfer baseline)	20.22%	4.96%
SimMemDA (full: WakeGAN+filter+memory)	57.03%	19.65%

Visualizations (e.g., t-SNE, heatmaps) confirm better domain alignment after WakeGAN’s translation and subsequent filtering. Detection bounding boxes are more accurately localized, and empirical analysis through ablation validates incremental value for each architectural component.

A plausible implication is that WakeGAN’s explicit spectral/structural constraints are critical for performance gains, as generic style transfer would fail to preserve wake features, thus impeding downstream detection.

6. Contextual Relationship with iWGAN and Related Models

WakeGAN’s architectural choices are contextually rooted in the inferential Wasserstein GAN (iWGAN) paradigm (Chen et al., 2021), with the style transfer objective aligned to cycle-consistent and duality-constrained schemes. The use of spectral and geometric constraints extends the reconstruction-centric formulation of iWGAN, adapting it for application-specific needs in SAR imagery. Notably, WakeGAN and iWGAN employ sample-wise quality measurements, structure/texture decompositions, and generative mappings bridged by learned latent codes. This suggests WakeGAN can be interpreted as a geometric/texture-aware instantiation of the iWGAN framework within a cross-modal adaptation context.

Potential misconceptions include assuming WakeGAN is a pure image translation model; its design, spectral losses, and feature filtering link it tightly to the problem structure of SAR wakes and to the inferential objectives in iWGAN. Its role within SimMemDA enables robust pseudo-supervision, outperforming vanilla GAN or CycleGAN-style approaches in maintaining annotated feature integrity.

7. Summary of Functional Integration within Domain Adaptation Pipelines

WakeGAN functions as the cornerstone in SimMemDA’s unsupervised domain adaptation, providing:

• Input-level domain alignment via dual-constrained structure-preserving style transfer,
• Instance-level selection based on feature similarity computed either via Euclidean or probabilistic measures,
• Confidence calibration for pseudo-labeling drawing on both historical feature memory and local feature geometry,
• Consistent, superior empirical performance evidenced by significant improvements in mean average precision metrics.

Its success in SAR wake detection tasks demonstrates the benefit of incorporating explicit frequency and geometry-aware modules and objective constraints, setting direction for future research in specialized generative adaptation for remote sensing and other modality-bridging applications (Gao et al., 14 Sep 2025).