Related papers: PDE-based numerical method for a limited angle X-r…
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.
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…
X-ray spectral fitting of astronomical sources requires convolving the intrinsic spectrum or model with the instrumental response. Standard forward modeling techniques have proven success in recovering the underlying physical parameters in…
Radon transform is widely used in physical and life sciences and one of its major applications is the X-ray computed tomography (X-ray CT), which is significant in modern health examination. The Radon inversion or image reconstruction is…
We propose a stable and fast reconstruction technique for parallel-beam (PB) tomographic X-ray imaging, relying on the discrete pseudo-polar (PP) Radon transform. Our main contribution is a resampling method, based on modern sampling…
Radon transform and its inverse operation are important techniques in medical imaging tasks. Recently, there has been renewed interest in Radon transform for applications such as content-based medical image retrieval. However, all studies…
Radon Transformation is generally used to construct optical image (like CT image) from the projection data in biomedical imaging. In this paper, the concept of Radon Transformation is implemented to reconstruct Electrical Impedance…
We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight…
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in…
A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested. The new implementation uses FFT for discrete sine transform and an interpolation step. The convergence of…
We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a…
We integrate a small and portable medical x-ray device with mechanical testing equipment to enable in-situ, non-invasive measurements of a granular material's response to mechanical loading. We employ an orthopedic C-arm as the x-ray source…
We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or…
Left-invariant PDE-evolutions on the roto-translation group $SE(2)$ (and their resolvent equations) have been widely studied in the fields of cortical modeling and image analysis. They include hypo-elliptic diffusion (for contour…
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…
X-ray tomography has applications in various industrial fields such as sawmill industry, oil and gas industry, chemical engineering, and geotechnical engineering. In this article, we study Bayesian methods for the X-ray tomography…
Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…
Performing X-ray computed tomography (CT) examinations with less radiation has recently received increasing interest: in medical imaging this means less (potentially harmful) radiation for the patient; in non-destructive testing of…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
We lay the foundations for a new fast method to reconstruct the electron density in x-ray scanning applications using measurements in the dark field. This approach is applied to a type of machine configuration with fixed energy sensitive…