Related papers: Modified Radon transform inversion using moments
The Discrete Periodic Radon Transform (DPRT) has been extensively used in applications that involve image reconstructions from projections. This manuscript introduces a fast and scalable approach for computing the forward and inverse DPRT…
Based on image moment theory, an approach for space-variant Shack-Hartmann wavefront reconstruction is presented in this article. The relation between the moment of a pair of subimages and the local transformation coefficients is derived.…
We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…
Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different…
In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction…
In this paper, we investigate the relations between the Radon and weighted divergent beam and cone transforms. Novel inversion formulas are derived for the latter two. The weighted cone transform arises, for instance, in image…
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…
We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In $\mathbb{R}^3$ it maps a function to its surface integrals over circular cones, and in $\mathbb{R}^2$ it maps a function to its…
We introduce an analytic method which stably reconstructs both components of a (sufficiently) smooth, real valued, vector field compactly supported in the plane from knowledge of its Doppler transform and its first moment Doppler transform.…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…
The reconstruction of electrical current densities from magnetic field measurements is an important technique with applications in materials science, circuit design, quality control, plasma physics, and biology. Analytic reconstruction…
In this work we study weighted Radon transforms in multidimensions. We introduce an analog of Chang approximate inversion formula for such transforms and describe all weights for which this formula is exact. In addition, we indicate…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
We compare the Radon transform in its standard and symplectic formulations and argue that the inversion of the latter can be performed more efficiently.
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.
The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
The limited angle Radon transform is notoriously difficult to invert due to its ill-posedness. In this work, we give a mathematical explanation that data-driven approaches can stably reconstruct more information compared to traditional…
Radiography is often used to probe complex, evolving density fields in dynamic systems and in so doing gain insight into the underlying physics. This technique has been used in numerous fields including materials science, shock physics,…
In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications,…