Dirichlet Splatting: Differentiable Rendering for Wave-Based Inverse Problems

arXiv cs.GR details Dirichlet Splatting, a new differentiable rendering approach aimed at wave-based inverse problems such as terahertz tomography, synthetic-aperture acoustics, and millimeter-wave radar. The core change is simple but important: instead of borrowing 3D Gaussian splats, the method uses the physically exact Dirichlet kernel from finite-window DFTs, paired with a surfel representation that carries area, normal, and material.

For developers, the interesting part is that this is not just a prettier approximation. Coherent sensing depends on phase and sidelobes, and the paper argues Gaussian footprints throw away both, which can break reconstruction by design. Dirichlet Splatting keeps the forward model aligned with the measurement physics while staying differentiable end to end.

The optimization side is equally specialized. The authors pair the renderer with Dirichlet Sliding Frank-Wolfe, which uses variable projection, residual dual certificates, certificate-driven hard replacement of low-utility surfels, and periodic low-resolution Levenberg-Marquardt correction to handle a rugged loss landscape.

The headline result is dense terahertz reconstruction: reflector centers are recovered to 0.018 bin RMSE, and the method is said to be 10-50x faster than waveform-level automatic differentiation. The exact practical payoff for game teams is indirect, but the work is relevant to anyone tracking differentiable rendering, inverse problems, and physically grounded splatting variants that could influence future capture, scanning, or simulation tools.