发表机构
University of California San Diego（加州大学圣地亚哥分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对波基相干成像，提出用物理精确的Dirichlet核替代高斯足迹，结合专用DSFW求解器，实现快速高精度太赫兹重建，比波形级自动微分快10-50倍。
AI 中文摘要
基于波的相干成像，包括太赫兹断层扫描、合成孔径声学和毫米波雷达，通过对有限长度信号进行傅里叶处理来形成图像，其精确点扩散函数不是高斯函数，而是Dirichlet核：复值、振荡且周期性的。然而，将3D高斯泼溅移植到相干传感在构造上会失败；高斯泼溅丢弃了旁瓣能量（占总能量的10-20%）以及控制反射器之间相干干涉的相位。我们的关键思想是用有限窗口DFT的物理精确Dirichlet核替换学习到的高斯足迹，并由携带面积、法线和材质的surfel调制，从而使渲染基元匹配测量物理而非近似它。我们将此基元与专用求解器Dirichlet滑动Frank-Wolfe（DSFW）配对，该求解器结合了变量投影、残差对偶证书和证书驱动的低效用surfel硬替换，并周期性地进行低分辨率耦合Levenberg-Marquardt校正，以导航破坏通用一阶优化器的崎岖损失景观。Dirichlet核允许O(1)闭式求值，因此前向模型与FFT真值匹配到机器精度，同时保持端到端可微。在密集太赫兹重建中，我们的方法将反射器中心恢复到0.018 bin RMSE，比波形级自动微分快10-50倍，而高斯泼溅则失败。
英文摘要
Wave-based coherent imaging, including terahertz tomography, synthetic-aperture acoustics, and millimeter-wave radar, forms images by Fourier-processing finite-length signals, with an exact point spread function that is not Gaussian but a Dirichlet kernel: complex-valued, oscillatory, and periodic. However, transplanting 3D Gaussian splatting to coherent sensing fails by construction; Gaussian splats discard the sidelobe energy (10-20% of the total) and the phase that governs coherent interference between reflectors. Our key idea is to replace the learned Gaussian footprint with the physically exact Dirichlet kernel of the finite-window DFT, modulated by a surfel that carries area, normal, and material, so that the rendering primitive matches the measurement physics instead of approximating it. We pair this primitive with a specialized solver, Dirichlet Sliding Frank-Wolfe (DSFW), that combines variable projection, residual dual certificates, and certificate-driven hard replacement of low-utility surfels, with periodic low-resolution coupled Levenberg-Marquardt correction, navigating the rugged loss landscape that breaks generic first-order optimizers. The Dirichlet kernel admits an O(1) closed-form evaluation, so the forward model matches FFT ground truth to machine precision while remaining differentiable end-to-end. On dense terahertz reconstruction, our method recovers reflector centers to 0.018 bin RMSE, 10-50x faster than waveform-level automatic differentiation, where Gaussian splats fail.
Comments19 pages, 13 figures, including appendices. Accepted for publication in ACM Transactions on Graphics
