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Complex-Valued 2D Gaussian Representation for Computer-Generated Holography

Complex-valued Gaussian primitives have recently been explored for representing holographic radiance fields in 3D novel view synthesis. In this work, we extend this line of research to the hologram optimization domain and propose a structured representation based on complex-valued 2D Gaussian primitives. Inspired by Gabor's theory, we show that our primitive attains the minimum space-frequency uncertainty and reduces the parameter search space by 5:1 compared to per-pixel parameterization. To enable end-to-end training, we develop a differentiable rasterizer for our representation, integrated with a GPU-optimized light propagation kernel in free space. Extensive experiments show that our method reduces VRAM usage by up to 30% and accelerates optimization by 50% over standard autodiff-based implementations, delivers up to 13 dB higher PSNR than prior Gaussian-based methods, and achieves up to 3200x faster rendering while maintaining reconstruction quality on par with existing CGH approaches. For evaluation, we introduce a conversion procedure that adapts our representation to practical hologram formats, including smooth and random phase-only holograms. By reducing the hologram parameter search space, our representation enables a more scalable hologram estimation in the next-generation computer-generated holography systems.

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