We present a Dual-Domain Equivariant Generative Adversarial Network (DDE-GAN) for multimodal CT-PET image synthesis. Traditional GAN-based approaches often operate solely in the spatial domain and ignore geometric consistency, resulting in limited structural fidelity. DDE-GAN addresses these challenges by jointly learning from both spatial and frequency (Fourier) domains, capturing complementary anatomical and spectral information. Furthermore, rotational equivariance embedded in the physics of the CT and PET measurements are integrated into the loss of both the generator and discriminator to ensure consistent responses under rotations, improving anatomical accuracy. A hierarchical dual-domain training strategy enforces intra- and inter-domain consistency through multi-stage loss functions. Evaluated on the HECKTOR 2022 CT-PET dataset, DDE-GAN achieves superior synthesis quality over baseline models for CT-PET image synthesis. The results demonstrate that combining dual-domain learning with geometric equivariance substantially enhances multimodal image synthesis accuracy and robustness, enabling practical applications in PET completion and data augmentation.

翻译：我们提出了一种用于多模态CT-PET图像合成的双域等变生成对抗网络（DDE-GAN）。传统基于GAN的方法通常仅在空间域中操作，忽略了几何一致性，导致结构保真度有限。DDE-GAN通过联合学习空间域和频率（傅里叶）域，捕获互补的解剖和光谱信息，从而解决这些挑战。此外，嵌入在CT和PET测量物理机制中的旋转等变性被集成到生成器和鉴别器的损失中，以确保在旋转变换下响应一致，从而提高解剖精度。一种层次化的双域训练策略通过多阶段损失函数强制执行域内和域间一致性。在HECKTOR 2022 CT-PET数据集上的评估表明，DDE-GAN在CT-PET图像合成中取得了优于基线模型的合成质量。结果表明，将双域学习与几何等变性相结合，显著提升了多模态图像合成的准确性和鲁棒性，为PET补全和数据增强等实际应用提供了支持。