论文标题
七维柠檬和苹果ra ra的微局部特性与康普顿散射断层扫描中的应用
Microlocal properties of seven-dimensional lemon and apple Radon transforms with applications in Compton scattering tomography
论文作者
论文摘要
我们对康普顿散射断层扫描（CST）的两种新颖的ra转变进行了微局部分析，该ra占二维苹果和柠檬表面的绘制映射为$ l^2 $函数。具体来说，我们表明苹果和柠檬的变换是椭圆形傅立叶积分运算符（FIO），它满足了Bolker条件。在分析了完整的七维案例之后，我们将注意力集中在带有固定中央轴的苹果和柠檬表面的子集上，其中$ n <7 $。这样的表面积分子集在机场行李和安全筛查中都有应用。当数据维度受到限制时，Apple变换被证明违反了Bolker条件，并且在Apple-lixder交叉点上发生了伪影。当函数的支持仅限于条带$ \ {0 <z <1 \} $时，柠檬转换显示可满足Bolker条件。
We present a microlocal analysis of two novel Radon transforms of interest in Compton Scattering Tomography (CST), which map compactly supported $L^2$ functions to their integrals over seven-dimensional sets of apple and lemon surfaces. Specifically, we show that the apple and lemon transforms are elliptic Fourier Integral Operators (FIO), which satisfy the Bolker condition. After an analysis of the full seven-dimensional case, we focus our attention on $n$-D subsets of apple and lemon surfaces with fixed central axis, where $n<7$. Such subsets of surface integrals have applications in airport baggage and security screening. When the data dimensionality is restricted, the apple transform is shown to violate the Bolker condition, and there are artifacts which occur on apple-cylinder intersections. The lemon transform is shown to satisfy the Bolker condition, when the support of the function is restricted to the strip $\{0<z<1\}$.
