论文标题
像素驱动的ra和扇形变换的收敛分析
Convergence analysis of pixel-driven Radon and fanbeam transforms
论文作者
论文摘要
本文提出了一个新型的数学框架，用于理解平行梁ra ra和扇形变换的像素驱动的方法，并表明可以获得$ l^2 $运算符规范中的正确离散策略，包括汇率 - 包括速率 - 。这些速率可以告知适当的策略以离散发生的域/变量，并首先是为ra换变换而建立的。特别是，将检测器离散与图像像素（这是标准实践）相同的大小可能不是理想的，实际上，渐近的像素比检测器会导致收敛。讨论了对限量角和稀疏角ra ra换变换的可能调整，并显示了类似的收敛结果。同样，收敛结果很容易扩展到一种新型像素驱动的方法，以实现扇形变换。讨论了离散化方案的数值方面，并特别表明，通过正确的离散策略，可以避免典型的高频伪像。
This paper presents a novel mathematical framework for understanding pixel-driven approaches for the parallel beam Radon transform as well as for the fanbeam transform, showing that with the correct discretization strategy, convergence - including rates - in the $L^2$ operator norm can be obtained. These rates inform about suitable strategies for discretization of the occurring domains/variables, and are first established for the Radon transform. In particular, discretizing the detector in the same magnitude as the image pixels (which is standard practice) might not be ideal and in fact, asymptotically smaller pixels than detectors lead to convergence. Possible adjustments to limited-angle and sparse-angle Radon transforms are discussed, and similar convergence results are shown. In the same vein, convergence results are readily extended to a novel pixel-driven approach to the fanbeam transform. Numerical aspects of the discretization scheme are discussed, and it is shown in particular that with the correct discretization strategy, the typical high-frequency artifacts can be avoided.
