On a reconstruction formula for spherical Radon transform: a microlocal analytic point of view
On a reconstruction formula for spherical Radon transform: a microlocal analytic point of view
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球Radon变换的重构公式：微局域分析的观点
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发表时间：
2014
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通讯作者：
Linh V. Nguyen
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作者：
Linh V. Nguyen
摘要设$$\mathcal R $$ R为球面Radon变换对以超曲面$$\mathcal S $$ s为中心的球集的限制。我们研究了由$$\mathcal R (f)$$ R(f)构造函数$$f$$ f的封闭形式公式。我们通过研究振荡积分来解决这个问题，振荡积分依赖于观测面$$\mathcal S $$ S作为参数。然后，我们推导了相关的闭型重构公式的各种微局部解析性质。
Abstract Let $$\mathcal R $$R be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface $$\mathcal S $$S. We study the construction of a function $$f$$f from $$\mathcal R (f)$$R(f) by a closed-form formula. We approach the problem by studying an oscillatory integral, which depends on the observation surface $$\mathcal S $$S as a parameter. We then derive various microlocal analytic properties of the associated closed-form reconstruction formula.