一种从Radon投影重建图像的新方法

从中心位于平面上的两个球面 Radon 变换重建函数

Reconstruction of a function from its two spherical Radon transforms with the centers on a plane

本文研究中心位于平面上的双数据球面 Radon 变换，证明其对 C(R^3) 中函数的单射性并给出利用局部球面积分数据的反演公式。

Inverting the spherical Radon transform for physically meaningful functions

In this paper we refer to the reconstruction formulas given in L.-E. Andersson's On the determination of a function from spherical averages, which are often used in applications such as SAR and SONAR. We demonstrate that the first one of these formulas does not converge given physically reasonable assumptions. An alternative is proposed and it is shown that the second reconstruction formula is well-defined but might be difficult to compute numerically.

The monogenic Hua-Radon transform and its inverse

The monogenic Hua-Radon transform is defined as an orthogonal projection on holomorphic functions in the Lie sphere. Extending the work of Sabadini and Sommen, J. Geom. Anal. 29 (2019), 2709-2737, we determine its reproducing kernel. Integrating this kernel over the Stiefel manifold yields a linear combination of the zonal spherical monogenics. Using the reproducing properties of those monogenics we obtain an inversion for the monogenic Hua-Radon transform.

利用Funk变换重构球面上定义的函数

Reconstruction of a function defined on a sphere using the Funk transform

本文针对球面上非偶连续函数，提出附加条件并研究双数据Funk变换的单射性，给出迭代反演公式，具有凸性理论、积分几何及球面断层扫描的理论意义，并应用于扩散加权磁共振成像。

Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions

We give new formulas for finding a compactly supported function $v$ on $\mathbb{R}^d$, $d\geq 1$, from its Fourier transform $\mathcal{F} v$ given within the ball $B_r$. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions (PSWFs). In multidimensions, well-known results of the Radon transform theory reduce the problem to the one-dimensional case. Related results on stability and convergence rates are also given.