Numerically robust tetrahedron-based tomographic forward and backward projectors on parallel architectures

TL;DR

This paper introduces a numerically robust, GPU-parallelizable ray-tracing method for tetrahedral mesh-based tomographic reconstruction, offering flexible, efficient alternatives to traditional voxel-based approaches.

Contribution

It develops a novel parallelizable ray-tracing algorithm specifically designed for tetrahedral domains in CT reconstruction, addressing numerical robustness and GPU efficiency.

Findings

Demonstrates improved reconstruction flexibility with tetrahedral meshes

Shows advantages over voxel-based methods in initial tests

Provides a robust solution for GPU-accelerated tomography

Abstract

X-ray tomographic reconstruction typically uses voxel basis functions to represent volumetric images. Due to the structure in voxel basis representations, efficient ray-tracing methods exist allowing fast, GPU accelerated implementations. Tetrahedral mesh basis functions are a valuable alternative to voxel based image representations as they provide flexible, inhomogeneous partitionings which can be used to provide reconstructions with reduced numbers of elements or with arbitrarily fine object surface representations. We thus present a robust parallelizable ray-tracing method for volumetric tetrahedral domains developed specifically for Computed Tomography image reconstruction. Tomographic image reconstruction requires algorithms that are robust to numerical errors in floating point arithmetic whilst typical data sizes encountered in tomography require the algorithm to be parallelisable in GPUs which leads to additional constraints on algorithm choices. Based on these considerations, this article presents numerical solutions to the design of efficient ray-tracing algorithms for the projection and backprojection operations. Initial reconstruction results using CAD data to define a triangulation of the domain demonstrate the advantages of our method and contrast tetrahedral mesh based reconstructions to voxel based methods.