Gaussian Wave Splatting in Holographic Rendering

• Gaussian Wave Splatting (GWS) is a method that converts Gaussian scene representations from neural rendering pipelines into complex holograms for photorealistic displays.
• It introduces a closed-form 2D Gaussian-to-hologram transform with occlusion support and an efficient Fourier-domain approximation using custom CUDA kernels.
• The framework is extended by a random-phase approach to enhance bandwidth utilization, defocus, parallax, and eyebox uniformity in holographic displays.

Gaussian Wave Splatting (GWS) is a computer-generated holography (CGH) framework that converts Gaussian scene representations, as optimized by recent neural rendering pipelines, into holograms for holographic display systems. In the formulation introduced for photorealistic scenes, GWS builds on Gaussian primitives recovered from a small number of photographs, derives a closed-form 2D Gaussian-to-hologram transform with occlusion support and alpha blending, and further derives an efficient Fourier-domain approximation that is parallelizable and implemented with custom CUDA kernels. The method is therefore situated at the intersection of neural scene representations, differentiable rendering, and holographic wavefield synthesis (Choi et al., 10 May 2025).

1. Definition and positioning within CGH

GWS was introduced as an efficient algorithm for turning Gaussian scene representations into holograms, rather than as a new Gaussian scene representation in itself. Its stated point of departure is that state-of-the-art neural rendering methods already optimize Gaussian scenes from a few photographs for novel-view synthesis; GWS reuses those Gaussians as the input to CGH. Unlike existing CGH algorithms, it is described as supporting accurate occlusions and view-dependent effects for photorealistic scenes by leveraging recent advances in neural rendering (Choi et al., 10 May 2025).

Within later holography literature, GWS is treated as a distinct CGH paradigm for holographic near-eye displays. That later framing emphasizes its importance precisely because it couples neural 3D representations with optical wave synthesis: Gaussian primitives become the bridge between scene reconstruction and interference-pattern generation on spatial light modulators (SLMs). A plausible implication is that GWS is best understood not as an isolated rendering trick, but as a pipeline-level connection between inverse scene reconstruction and forward hologram computation (Chao et al., 24 Aug 2025).

2. Gaussian primitives and the standard forward model

In the later formalization of standard GWS, the input is a set of Gaussian primitives, typically obtained from optimized 2D Gaussian splats. Each primitive $i$ is described by a mean position $\mu_i \in \mathbb{R}^3$, covariance $\Sigma_i = R_i S_i S_i^\mathsf{T} R_i^\mathsf{T}$, opacity $o_i$, and color $c_i$. The Gaussians are depth-sorted front-to-back relative to the SLM or camera, which makes occlusion handling compatible with front-to-back compositing (Chao et al., 24 Aug 2025).

The standard GWS pipeline is summarized as analytically computing each Gaussian’s wavefront, propagating each wavefront to the SLM plane using the angular spectrum method, and alpha-compositing them front-to-back. In that description, hologram formation is written as

$$u_{\textrm{SLM}}(x) = \sum_i^N \mathcal{P}\Big(c_i\, o_i\, |u_i(x)|\, T_i(x)\, e^{ik z_i}; -z_i\Big),$$

with transmittance

$$T_i(x) = \prod_{j=1}^{i-1} \left(1 - o_j |u_j(x)| \right).$$

Here $u_i(x)$ is the wavefront of the $i$-th Gaussian, $z_i$ is its depth, $\mu_i \in \mathbb{R}^3$0, and $\mu_i \in \mathbb{R}^3$1 denotes propagation by distance $\mu_i \in \mathbb{R}^3$2. This formulation makes explicit that GWS combines per-primitive wave synthesis with visibility-aware compositing rather than relying on classical polygonal CGH pipelines (Chao et al., 24 Aug 2025).

3. Closed-form Gaussian-to-hologram transform and computational organization

A central contribution of GWS is the derivation of a closed-form solution for a 2D Gaussian-to-hologram transform that supports occlusions and alpha blending. This is the key analytical step that turns projected Gaussian primitives into wave contributions suitable for hologram synthesis. The same work also derives, “inspired by classic computer graphics techniques,” an efficient approximation of that process in the Fourier domain, emphasizing that the approximation is easily parallelizable and is implemented using custom CUDA kernels (Choi et al., 10 May 2025).

This division between an analytical transform and a Fourier-domain approximation is structurally important. The closed-form result supplies an explicit Gaussian-to-wave mapping, while the Fourier-domain approximation supplies a GPU-oriented realization strategy. This suggests that GWS occupies a hybrid computational regime: it inherits continuous Gaussian parameterization from neural rendering, but pursues CGH throughput using a splatting-like parallelization strategy rather than purely iterative wave-optics solvers. The original description does not report a separate algorithmic taxonomy, but the stated design clearly aligns analytic tractability with high-throughput implementation (Choi et al., 10 May 2025).

4. Occlusion handling, view dependence, and the smooth-phase model

The original formulation of GWS states that it supports accurate occlusions and view-dependent effects for photorealistic scenes. In context, this claim distinguishes it from existing CGH algorithms by tying hologram generation to Gaussian scene models already optimized for photorealistic neural rendering, where occlusion structure and appearance variation are encoded in the underlying representation (Choi et al., 10 May 2025).

Subsequent work characterizes the standard formulation as smooth-phase GWS, or GWS-SP. In that description, the phase of each Gaussian wavefront is assumed to be approximately constant or smooth,

$\mu_i \in \mathbb{R}^3$3

so the synthesized hologram is itself smooth-phase. That later analysis argues that smooth-phase holograms concentrate energy near low spatial frequencies in the angular spectrum, under-utilize the SLM space-bandwidth product, produce unnatural defocus blur, and do not support angular emission variation well. The same source further argues that the original alpha-wave blending scheme was designed for smooth-phase coherent wavefronts and is not naturally compatible with random phase (Chao et al., 24 Aug 2025).

Taken together, these statements indicate a specific historical trajectory. GWS improves on earlier CGH pipelines by bringing occlusion-aware Gaussian scene models into holography, yet later work argues that the standard optical phase model remains restrictive. This suggests that GWS’s novelty lies less in abandoning coherent holography than in making Gaussian neural scene representations operable within it.

5. Random-phase GWS and the expansion of the framework

A major extension is Random-phase Gaussian Wave Splatting (GWS-RP), which replaces the smooth-phase assumption with structured random phase. Its stated objective is improved bandwidth utilization, with the reported effects of increasing eyebox size, reconstructing accurate defocus blur and parallax, and supporting time-multiplexed rendering to suppress speckle artifacts. The extension highlights two core additions: a fundamentally new wavefront compositing procedure and an alpha-blending scheme specifically designed for random-phase Gaussian primitives, intended to ensure physically correct color reconstruction and robust occlusion handling (Chao et al., 24 Aug 2025).

In GWS-RP, reconstructed intensity is averaged over time-multiplexed frames,

$\mu_i \in \mathbb{R}^3$4

and the composite wavefront is built by a back-to-front recursion,

$\mu_i \in \mathbb{R}^3$5

with

$\mu_i \in \mathbb{R}^3$6

The theoretical distinction drawn in that work is that smooth-phase GWS is exact in the amplitude domain, whereas random-phase GWS-RP is exact in the intensity domain. The same analysis attributes broader angular spectrum support, more natural defocus behavior, improved parallax, and larger eyebox uniformity to the random-phase formulation, while using time multiplexing to reduce speckle (Chao et al., 24 Aug 2025).

From an encyclopedic standpoint, GWS-RP is not a separate lineage unrelated to GWS; it is an optical generalization of the original framework. The extension preserves Gaussian primitives and compositing logic, but revises the phase statistics and the correctness criterion for blending.

6. Relation to adjacent “wave” and high-frequency Gaussian methods

The term “Gaussian Wave Splatting” can be confused with other Gaussian-splatting variants that also invoke waves, frequency structure, or high-frequency detail. In the current literature, however, those methods are technically distinct. “Wavelet-GS: 3D Gaussian Splatting with Wavelet Decomposition” integrates 3D wavelet decomposition into point-cloud processing and 2D wavelet decomposition into image supervision for scene reconstruction; it is described as GWS-like in spirit, but it targets frequency-decoupled 3D reconstruction rather than CGH or wavefield synthesis (Zhao et al., 16 Jul 2025).

Likewise, “3D Gabor Splatting” augments Gaussian kernels with Gabor noise and spatially fluctuating wave functions to represent high-frequency surface texture inside a primitive; its “wave” content is a texture-modeling device rather than an optical propagation model (Watanabe et al., 15 Apr 2025). “TextureSplat” explicitly is not a wave-based method and does not target wave optics, interference effects, or phase-aware rendering; it is a reflective inverse-rendering extension of 2D Gaussian Splatting with per-primitive texture maps (Younes et al., 16 Jun 2025). “IBGS: Image-Based Gaussian Splatting” is similarly not directly wave-based, instead modeling each pixel as a base 3DGS color plus a learned residual inferred from neighboring training images (Nguyen et al., 18 Nov 2025).

These distinctions matter because GWS is fundamentally a holographic rendering method. Its defining concern is the conversion of Gaussian scene primitives into complex wavefields and ultimately into SLM-displayable interference patterns. By contrast, wavelet, Gabor, texture, and image-based Gaussian methods remain within the broader novel-view-synthesis and inverse-rendering family, even when they address high-frequency structure or view-dependent appearance. A plausible implication is that GWS should be classified primarily under Gaussian-based CGH rather than under general Gaussian-splatting appearance modeling.