用基函数加速图像投影计算，提升重建精度与效率。
Generalized Ray Tracing with Basis functions for Tomographic Projections
- 基于基函数的射线追踪法，高效计算重叠区域的投影积分
- 在任意投影几何下实现前向与反向算子计算，提升重建质量
- 特别适用于样条表示的图像，适合医学成像等逆问题场景
本文致力于高效精确地计算由一般平移基函数线性组合表示、通常存在重叠的图像的X射线投影。通过适配射线追踪技术——一种高效的线积分计算方法——实现这一目标。特别关注图像以样条形式表达的情形。所提方法适用于任意投影几何，可在一组任意直线构成的集合上计算前向与反向算子。实验验证了其在图像重建逆问题中的有效性，并在给定重建网格分辨率下最大化图像质量。
原文摘要 · Abstract (English)
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.
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