论文标题
Minkowski空间中损坏的非亚伯X射线变换的稳定性估计值
Stability estimate for the broken non-abelian X-ray transform in Minkowski space
论文作者
论文摘要
我们研究了Minkowski空间中损坏的非亚伯X射线变换。这种转换作用于因果钻石上的冬宫连接的空间，并且已知具有无限维度的外观。我们显示了一个考虑量规的稳定性估计，从而导致了转换注射率的新证明。我们的证明使我们考虑了一种特殊的连接类型，我们称之为光线链接连接。然后，我们表明我们可以通过Yesiy噪声测量其X射线转换数据来始终如一地恢复光线连接。
We study the broken non-abelian X-ray transform in Minkowski space. This transform acts on the space of Hermitian connections on a causal diamond and is known to be injective up to an infinite-dimensional gauge. We show a stability estimate that takes into account the gauge, leading to a new proof of the transform's injectivity. Our proof leads us to consider a special type of connections that we call light-sink connections. We then show that we can consistently recover a light-sink connection from noisy measurement of its X-ray transform data through Bayesian inversion.
