Related papers: Irregular sampling and the Radon transform
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 derive an explicit inversion algorithm for the spherical Radon transform in odd dimensions with partial radial data. We prove that the reconstruction of the unknown function can be reduced to solving ordinary differential equations,…
Deformable image registration is a standard engineering problem used to determine the distortion experienced by a body by comparing two images of it in different states. This study introduces two new DIR methods designed to capture…
A general method for analytic inversion in integral geometry is proposed. All classical and some new reconstruction formulas of Radon-John type are obtained by this method. No harmonic analysis and PDE is used.
Computer vision tasks require processing large amounts of data to perform image classification, segmentation, and feature extraction. Optical preprocessors can potentially reduce the number of floating point operations required by computer…
We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy etc. Since the acquired tomographic data is…
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…
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…
We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in $\rn$. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions…
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being…
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions and derive an explicit…
Image moments are weighted sums over pixel values in a given image and are used in object detection and localization. Raw image moments are derived directly from the image and are fundamental in deriving moment invariants quantities. The…
Recovering a function from its spherical Radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies, including SAR, ultrasound imaging, and photo- and…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
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…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…