The weighted doppler transform
The weighted doppler transform
复制标题
加权多普勒变换
DOI：
10.3934/ipi.2010.4.111
复制
发表时间：
2009
影响因子：
1.3
通讯作者：
P. Stefanov
中科院分区：
文献类型：
--
作者：
S. Holman;P. Stefanov
我们考虑基于一系列曲线 $\Gamma$ 上的加权多普勒变换在简单黎曼流形上恢复协矢量场的层析成像问题。这是衰减多普勒变换的推广。在权重函数的条件下，一组通用权重和曲线族的唯一性被证明。特别是如果权重函数永远不为零，并且其沿 $\Gamma$ 曲线的导数永远不为零，则满足此条件。
We consider the tomography problem of recovering a covector field on a simple Riemannian manifold based on its weighted Doppler transformation over a family of curves $\Gamma$. This is a generalization of the attenuated Doppler transform. Uniqueness is proven for a generic set of weights and families of curves under a condition on the weight function. This condition is satisfied in particular if the weight function is never zero, and its derivatives along the curves in $\Gamma$ are never zero.