# Hologram Representation via Quadratic Phase Gaussian Splatting

arXiv: https://arxiv.org/abs/2609.11434 · HTML: https://mlsanity.com/paper/2609.11434/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 5 of 5)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models](https://mlsanity.com/paper/2208.06677/) (2022)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [ColorVideoVDP: A visual difference predictor for image, video and display distortions](https://mlsanity.com/paper/2401.11485/) (2024)

## Abstract (arXiv)

We introduce Complex-Valued Quadratic Phase Gaussian (CVQPG), a novel hologram representation method that augments each 2D Gaussian primitive with a quadratic phase profile controlled by a learnable curvature parameter. Against the planar Gaussian baseline, CVQPG improves the average PSNR of holographic reconstructions by 0.19 dB (RGB) and 0.33 dB (grayscale) at equal primitive counts, and by 0.05 dB (RGB) and 0.08 dB (grayscale) at equal parameter counts, where it still leads in all visual quality metrics. Our frequency-domain analysis shows that CVQPG better preserves the mid-to-high frequency band of natural images, where the reconstruction MSE drops by up to 11% (RGB) and 22% (grayscale), indicating that modulating primitive wavefronts is an effective and lightweight enhancement.