Related papers: Modelling x-ray tomography using integer compositi…
Let A be any set of positive integers and n a positive integer. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. We derive generating functions for the number of compositions of n with…
X-ray single particle imaging involves the measurement of a large number of noisy diffraction patterns of isolated objects in random orientations. The missing information about these patterns is then computationally recovered in order to…
X-ray tomography is a powerful volumetric imaging technique, but detailed three dimensional (3D) imaging requires the acquisition of a large number of individual X-ray images, which is time consuming. For applications where spatial…
We consider a discrete stochastic process, indexed by lines through the unit disk in the plane, which models the observed photon counts in a medical X-ray tomography scan. We first prove a functional law of large numbers, showing that this…
The X-ray of a permutation is defined as the sequence of antidiagonal sums in the associated permutation matrix. X-rays of permutation are interesting in the context of Discrete Tomography since many types of integral matrices can be…
X-ray microscopy (XRM) is commonly used to obtain three-dimensional information on internal microstructure, but the imaging pipeline introduces noise, redundancy and information loss at multiple stages. This paper treats the XRM workflow as…
X-ray imaging can be efficiently used for high-throughput in-line inspection of industrial products. However, designing a system that satisfies industrial requirements and achieves high accuracy is a challenging problem. The effect of many…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map…
Multi-energy X-ray tomography is studied for decomposing three materials using three X-ray energies and a classical energy-integrating detector. A novel regularization term comprises inner products between the material distribution…
X-ray spectroscopy is a powerful technique for the analysis of the energy distribution of X-rays from astrophysical sources. It allows for the study of the properties, composition, and physical processes taking place at the site of…
We give a geometric approach to integer factorization. This approach is based on special approximations of segments of the curve that is represented by $y=n/x$, where $n$ is the integer whose factorization we need.
Among all the sub-sections in a typical radiology report, the Clinical Indications, Findings, and Impression often reflect important details about the health status of a patient. The information included in Impression is also often covered…
An M-partition of a positive integer m is a partition with as few parts as possible such that any positive integer less than m has a partition made up of parts taken from that partition of m. This is equivalent to partitioning a weight m so…
We propose an ambitious new method that models the intracluster medium in clusters of galaxies as a set of X-ray emitting smoothed particles of plasma. Each smoothed particle is described by a handful of parameters including temperature,…
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…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It refines previous contributions, in which the preprocessing of…
X-ray Thomson scattering (XRTS) has emerged as a widely used diagnostics for extreme states of matter in a great variety of situations, and over a broad range of parameters. The standard approach for the interpretation of XRTS measurements…
X-Ray based computed tomography (CT) is a well-established technique for determining the three-dimensional structure of an object from its two-dimensional projections. In the past few decades, there have been significant advancements in the…