Donsub Rim
We give an exact inversion formula for the approximate discrete Radon transform introduced in [Brady, SIAM J. Comput., 27(1), 107--119] that is of cost $O(N \log N)$ for a square 2D image with $N$ pixels and requires only partial data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Inversion of the elliptical Radon transform arising in migration imaging using the regular Radon transform
本文研究了在迁移成像中出现的椭圆Radon变换，通过与常规Radon变换的关系推导了其逆变换公式，并通过二维数值模拟验证了算法有效性。
Exact inversion of the conical Radon transform with a fixed opening angle
本文研究了圆锥Radon变换的反演问题，提出在二维和三维空间中具有固定开角和垂直轴的反演公式，并通过数值模拟验证了算法效率。
We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev duality products and to a new family of probing functions. The fractional order duality product proves to be able to greatly enhance the robustness of the reconstructions in some practically important but severely ill-posed inverse problems associated with the Radon transform. We present a detailed analysis to better understand the performance of the new pr…
In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST). This new system is made of a single detector rotating around a fixed source. Unlike some previous CST, no collimator is used at the detector. Such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the associated Radon transform is a family of double circular arcs. As first main theoretical result, an analytic inversion formula is established for this new Radon transform. This is achieved throu…
On an Analytical Inversion Formula for the Modulo Radon Transform
针对模 Radon 变换，本文通过联系 Radon 变换 Laplacian 的 Poisson 问题与滤波反投影，提出解析反演公式及离散算法 LMU-FBP，并以数值实验验证。
We study the inversion of the conical Radon which integrates a function in three-dimensional space from integrals over circular cones. The conical Radon recently got significant attention due to its relevance in various imaging applications such as Compton camera imaging and single scattering optical tomography. The unrestricted conical Radon transform is over-determined because the manifold of all cones depends on six variables: the center position, the axis orientation and the opening angle of the cone. In this work, we consider a particular restricted transform using triple line sensors whe…
An approach to the spherical mean Radon transform with detectors on a line
本文提出了一种称为一致性方法的新方法，用于2D球面Radon变换的逆问题，通过证明重建具有局部描述并找到新的迭代公式，为从线L上圆心的球面均值恢复完全支持于线L一侧的未知函数提供了实用算法。
The spherical mean Radon transform with centers on cylindrical surfaces
本文研究了圆柱面上限制积分中心的球面Radon变换的反演问题，通过分解为低维球面Radon变换，提出高效重建算法，适用于一般圆柱域及特殊圆柱体，实现O(N^(4/3))次浮点运算。
Image reconstruction from radially incomplete spherical Radon data
本文研究了球面Radon变换在球面上的反演问题，提出在径向不完整数据下可唯一恢复球壳中的图像函数，并展示了在不同支持区域的重建方法和算法。
Analytic inversion of a conical Radon transform arising in application of Compton cameras on the cylinder
本文研究了在圆柱体上顶点位于圆柱轴上的锥形Radon变换的解析反演方法，并探讨了V线变换在特定条件下的应用。
Exact reconstruction formulas for a Radon transform over cones
本文研究了考虑康普顿散射的锥形Radon变换，推导出一种滤波反投影类型的精确重建公式，用于逆变换。
Fourier-Domain Inversion for the Modulo Radon Transform
本文针对模Radon变换的折叠投影重建问题，提出具有数学保证的傅里叶域反演算法，可在更低采样率和未知模阈值下低复杂度、鲁棒恢复，并经原型模ADC硬件验证。
The Funk-Radon transform for hyperplane sections through a common point
本文研究了超平面截面通过公共点的Funk-Radon变换，通过与经典Funk-Radon变换的关系，给出了该变换的单射性和范围特征。
The Radon Transform over Cones with Vertices on the Sphere and Orthogonal Axes
本文研究了顶点位于n维空间球面上的圆锥积分变换的可逆性，发展了基于级数展开和降维到广义阿贝尔型一维积分方程的反演方法，并推导了广义阿贝尔方程的唯一性结果。
Phantoms can serve as a gold standard for the validation of MRI numerical methods. In some special cases, it is possible to compute analytically the Radon transform, or sinogram, of a phantom. In this work, we present analytical formulae to compute the exact sinograms of three classes of phantoms. We compare the use of the discrete Radon transform, that yields an approximate sinogram, and the correspondent analytical sinogram for image reconstruction.
Irregular Sampling of the Radon Transform of Bandlimited Functions
研究带限函数Radon变换的不规则极坐标采样精确重建条件，证明Radon变换为连续L2算子，并讨论Beurling-Malliavin条件与Jaffard密度条件对重建的影响。
Variational regularization of the weighted conical Radon transform
本文研究了具有顶点在球面上的加权锥形Radon变换的逆问题，通过变分正则化方法实现了稳定反演，并比较了不同正则化项对锥形Radon数据重建质量的影响。
Analysis of view aliasing for the generalized Radon transform in $\mathbb R^2$
本文针对平面广义Radon变换，推导了分段光滑函数从视图方向离散数据重建时的视图混叠伪影渐近公式，无需带限假设，数值实验验证了其准确性。
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out. Geometric properties of the kernel and their implications for computer implementation are discussed. Suggestions are made for applications and an example is presented.
This paper presents a novel mathematical framework for understanding pixel-driven approaches for the parallel beam Radon transform as well as for the fanbeam transform, showing that with the correct discretization strategy, convergence - including rates - in the $L^2$ operator norm can be obtained. These rates inform about suitable strategies for discretization of the occurring domains/variables, and are first established for the Radon transform. In particular, discretizing the detector in the same magnitude as the image pixels (which is standard practice) might not be ideal and in fact, asymp…
A Frame Decomposition of the Funk-Radon Transform
本文提出一种基于三角多项式的Funk-Radon变换框架分解，作为奇异值分解的灵活替代，用于反演并经过数值实验验证。
Remarks on the general Funk-Radon transform and thermoacoustic tomography
研究光滑流形中一族超曲面定义的一般积分变换的性质，包括Sobolev范数估计、值域条件和积分变换核的逼近定理，并讨论在热/光/光声断层成像中出现的球面平均变换的应用。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。