破碎射线变换：附加性质和新的反演公式
The Broken Ray Transform: Additional Properties and New Inversion Formula
摘要：
断裂射线变换（BRT）的重要性是由于其出现在许多模态跨越光学，X射线和核成像。当数据由分散位置索引时，BRT是线性和移位不变的。将快速公交系统作为一个线性系统进行分析，为研究逆问题提供了一个新的视角。在这个框架中，我们对比先前的反演公式，并确定数值问题。这也有实际的好处。我们澄清的范围内所需的数据进行全球重建分解的BRT锥束变换的线性组合。此外，我们利用二维傅里叶变换推导出新的反演公式，计算效率为任意散射角。数值模拟的结果。
英文摘要：
The significance of the broken ray transform (BRT) is due to its occurrence in a number of modalities spanning optical, x-ray, and nuclear imaging. When data are indexed by the scatter location, the BRT is both linear and shift invariant. Analyzing the BRT as a linear system provides a new perspective on the inverse problem. In this framework we contrast prior inversion formulas and identify numerical issues. This has practical benefits as well. We clarify the extent of data required for global reconstruction by decomposing the BRT as a linear combination of cone beam transforms. Additionally we leverage the two dimensional Fourier transform to derive new inversion formulas that are computationally efficient for arbitrary scatter angles. Results of numerical simulations are presented.
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