SIAM Journal on Imaging Sciences, Volume 13, Issue 2, Page 746-774, January 2020.
Here we present a novel microlocal analysis of a new toric section transform which describes a two-dimensional image reconstruction problem in Compton scattering tomography and airport baggage screening. By an analysis of two separate limited data problems for the circle transform and using microlocal analysis, we show that the canonical relation of the toric section transform is 21. This implies that there are image artifacts in the filtered backprojection reconstruction. We provide explicit expressions for the expected artifacts and demonstrate these by simulations. In addition, we prove injectivity of the forward operator for $L^\infty$ functions supported inside the open unit ball. We present reconstructions from simulated data using a discrete approach and several regularizers with varying levels of added pseudorandom noise.

中文翻译：

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康普顿断层扫描问题的微观局部分析

SIAM影像科学杂志，第13卷，第2期，第746-774页，2020年1月。
在这里，我们介绍了一种新的复曲面截面变换的新型微局部分析，该变换描述了康普顿散射断层扫描和机场行李筛查中的二维图像重建问题。通过对两个单独的有限数据问题进行圆变换分析并使用微局部分析，我们表明复曲面截面变换的规范关系为21。这意味着在滤波后的反投影重建中存在图像伪像。我们为预期的工件提供了明确的表达式，并通过仿真进行了演示。另外，我们证明了在开放单位球内支持的$ L ^ \ infty $函数的前向运算符的内插性。我们提出了使用离散方法和几种具有不同伪随机噪声电平的正则器从模拟数据重构的方法。