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.
@article{arxiv.2503.20907,
title = {Generalized Ray Tracing with Basis functions for Tomographic Projections},
author = {Youssef Haouchat and Sepand Kashani and Philippe Thévenaz and Michael Unser},
journal= {arXiv preprint arXiv:2503.20907},
year = {2025}
}