An identity for triplets of double Hilbert transforms, with applications to the attenuated Radon transform

Str?mberg J.-O.; Andersson J.

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An identity for triplets of double Hilbert transforms, with applications to the attenuated Radon transform

机译：双重Hilbert变换的三元组的标识，并应用于衰减的Radon变换

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We consider an elementary identity for double singular integrals in the plane and show that one can apply this to deduce inversion and product formulae for the Hilbert transform and inversion formulae for the affine and weighted Radon transforms. We will be able to allow many of the previously known weights for which there is an inversion formula for the weighted Radon transform and also pose some new conditions on which weights that can be used.

机译：我们考虑平面中双奇异积分的基本身份，并表明可以将其用于推导Hilbert变换的反演和乘积公式以及仿射和加权Radon变换的反演公式。我们将能够允许许多先前已知的权重，对于这些权重，存在一个加权Radon变换的反演公式，并且还提出了一些可以使用权重的新条件。

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《Inverse Problems: An International Journal of Inverse Problems, Inverse Methods and Computerised Inversion of Data》 |2012年第12期|共25页
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Str?mberg J.-O.; Andersson J.;
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正文语种 eng
中图分类物理学;
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1. An identity for triplets of double Hilbert transforms, with applications to the attenuated Radon transform [J] . Str?mberg J.-O., Andersson J. Inverse Problems: An International Journal of Inverse Problems, Inverse Methods and Computerised Inversion of Data . 2012,第12期

机译：双重Hilbert变换的三元组的标识，并应用于衰减的Radon变换
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机译：衰减的RA变换：理论和在医学和生物学中的应用。
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An identity for triplets of double Hilbert transforms, with applications to the attenuated Radon transform

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