多频辐射源沿一条直线的最优恢复
Optimal recovery of a radiating source with multiple frequencies along one line
摘要：
我们研究了一个逆问题，其中一个未知的辐射源，观察与准直探测器沿一条线和介质具有已知的衰减。该研究的动机是在SPECT和射束硬化中的应用。如果进行测量的频率范围在一个开集，我们表明，源密度是唯一确定的这些测量平均超过levelsets的综合衰减。这导致广义拉普拉斯变换。我们还讨论了一些数值方法，并通过几个例子证明了结果。
英文摘要：
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.
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