Local inversion of the sonar transform regularized by the approximate inverse
Local inversion of the sonar transform regularized by the approximate inverse
复制标题
通过近似逆函数正则化的声纳变换的局部反演
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
T. Schuster
中科院分区：
文献类型：
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作者：
E. T. Quinto;A. Rieder;T. Schuster
给出了一种新的以平面为中心的球均变换的重构方法，也称为声纳变换。标准反演公式需要所有球体的数据，但通常，数据是有限的，因为中心和半径位于一个紧凑的集合中。我们的重建算子是局部的，因为要在 处重建，只需要经过 附近的球体，并且该算子重建奇点，例如对象边界。给出了重建算子的微局部性质，包括其作为伪微分算子的符号。该方法使用近似逆来实现，并给出了重构。根据重建算子的微局部属性来评估它们。
A new reconstruction method is given for the spherical mean transform with centers on a plane in which is also called the sonar transform. Standard inversion formulas require data over all spheres, but typically, the data are limited in the sense that the centers and radii are in a compact set. Our reconstruction operator is local because, to reconstruct at , one needs only spheres that pass near , and the operator reconstructs singularities, such as object boundaries. The microlocal properties of the reconstruction operator, including its symbol as a pseudodifferential operator, are given. The method is implemented using the approximate inverse, and reconstructions are given. They are evaluated in light of the microlocal properties of the reconstruction operator.