SplineSplat: 3D Ray Tracing for Higher-Quality Tomography

We propose a method to efficiently compute tomographic projections of a 3D volume represented by a linear combination of shifted B-splines. To do so, we propose a ray-tracing algorithm that computes 3D line integrals with arbitrary projection geometries. One of the components of our algorithm is a neural network that computes the contribution of the basis functions efficiently. In our experiments, we consider well-posed cases where the data are sufficient for accurate reconstruction without the need for regularization. We achieve higher reconstruction quality than traditional voxel-based methods.

A Statistical Benchmark for Diffusion Posterior Sampling Algorithms

We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms for Bayesian linear inverse problems. The benchmark synthesizes signals from sparse L\'evy-process priors whose posteriors admit efficient Gibbs methods. These Gibbs methods can be used to obtain gold-standard posterior samples that can be compared to the samples obtained by the DPS algorithms. By using the Gibbs methods for the resolution of the denoising problems in the reverse diffusion, the framework also isolates the error that arises from the approximations to the likelihood score. We instantiate the benchmark with the minimum-mean-squared-error optimality gap and posterior coverage tests and provide numerical experiments for popular DPS algorithms on the inverse problems of denoising, deconvolution, imputation, and reconstruction from partial Fourier measurements. We release the benchmark code at https://github.com/zacmar/dps-benchmark. The repository exposes simple plug-in interfaces, reference scripts, and config-driven runs so that new algorithms can be added and evaluated with minimal effort. We invite researchers to contribute and report results.

Generalized Ray Tracing with Basis functions for Tomographic Projections

This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray tracing, which is one of the most efficient methods to compute line integrals. In our work, the cases in which the image is expressed as a spline are of particular relevance. The proposed implementation is applicable to any projection geometry as it computes the forward and backward operators over a collection of arbitrary lines. We validate our work with experiments in the context of inverse problems for image reconstruction and maximize the image quality for a given resolution of the reconstruction grid.