Related papers: Tomography: mathematical aspects and applications
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
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 present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography. We first demonstrate that the truncated singular value decomposition-based…
In this article, we consider the limited data problem for spherical mean transform. We characterize the generation and strength of the artifacts in a reconstruction formula. In contrast to the third's author work [Ngu15b], the observation…
X-ray tomographic image reconstruction consists of determining an object function from its projections. In many applications such as non-destructive testing, we look for a fault region (air) in a homogeneous, known background (metal). The…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…
We introduce a mathematical model for ultrasound modulated optical tomography and present a simple reconstruction scheme for recovering the spatially varying optical absorption coefficient from scanning measurements with narrowly focused…
The following two inversion methods for Radon-like transforms are widely used in integral geometry and related harmonic analysis. The first method invokes mean value operators in accordance with the classical Funk-Radon-Helgason scheme. The…
Modern tomography involves gathering projection data from multiple directions and feeding them into a software algorithm for tomographic reconstruction. We focus our study on image reconstruction from Radon data in the setting of…
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…
Progress in the reconstruction for atom probe tomography has been limited since the first implementation of the protocol proposed by Bas et al. in 1995. This approach, and those subsequently developed, assume that the geometric parameters…
Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental…
We are going to study some conditions on which the Radon transform and its dual are invertible. Two function spaces are introduced that the Radon transform on which is bijective linear operator. In this regards, a reconstruction formula is…
Attenuated Radon projections with respect to the weight function $W_\mu(x,y) = (1-x^2-y^2)^{\mu-1/2}$ are shown to be closely related to the orthogonal expansion in two variables with respect to $W_\mu$. This leads to an algorithm for…
Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes…
In material testing applications, Computed Tomography is a well established imaging technique that allows the recovery of the attenuation map of an object. Conventional modalities exploit only primary radiation and although in the energy…
The paper contains a simple approach to reconstruction in Thermoacoustic and Photoacoustic Tomography. The technique works for any geometry of point detectors placement and for variable sound speed satisfying a non-trapping condition. A…