Related papers: Modelling x-ray tomography using integer compositi…
In this paper we broadly consider techniques which utilize projections on rays for data collection, with particular emphasis on optical techniques. We formulate a variety of imaging techniques as either special cases or extensions of…
X-ray scattering patterns from emerging single particle experiments have commonly many missing or contaminated pixels. This complicates different analyses including projections on Fourier or other basis functions (for noise suppression,…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
In three-dimensional models obtained by photogrammetry of existing structures, all of the shapes that the eye can select cannot always find their equivalents in the geometric components of the model. However, the matching of meaningful…
A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate…
We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…
A \Def{composition} of a positive integer $n$ is a $k$-tuple $(\l_1, \l_2, \dots, \l_k) \in \Z_{> 0}^k$ such that $n = \l_1 + \l_2 + \dots + \l_k$. Our goal is to enumerate those compositions whose parts $\l_1, \l_2, \dots, \l_k$ avoid a…
In recent scene recognition research images or large image regions are often represented as disorganized "bags" of features which can then be analyzed using models originally developed to capture co-variation of word counts in text.…
In this paper we present a generating function approach to two counting problems in elementary quantum mechanics. The first is to find the total ways of distributing identical particles among different states. The second is to find the…
Starting from three-dimensional volume data of a granular packing, as e.g. obtained by X-ray Computed Tomography, we discuss methods to first detect the individual particles in the sample and then analyze their properties. This analysis…
We describe a method aiming at increasing the dynamic range of X-ray detectors. Two X-ray exposures of an object are acquired at different dose levels and constitute the only input data. The values of the parameters which are needed to…
X-ray imaging is the most popular medical imaging technology. While x-ray radiography is rather cost-effective, tissue structures are superimposed along the x-ray paths. On the other hand, computed tomography (CT) reconstructs internal…
We propose approaches based on deep learning to localize objects in images when only a small training dataset is available and the images have low quality. That applies to many problems in medical image processing, and in particular to the…
Enabled by x-ray free-electron lasers, nonlinear optical phenomena can be explored in the x-ray domain nowadays. Among the multitude of newly accessible processes, this theoretical study focuses parametric x-ray optical wavemixing for…
X-ray interferometry is an emerging imaging modality with a wide variety of potential clinical applications, including lung imaging. A grating interferometer uses a diffraction grating to produce a periodic interference pattern and measures…
Modern technology for producing extremely bright and coherent X-ray laser pulses provides the possibility to acquire a large number of diffraction patterns from individual biological nanoparticles, including proteins, viruses, and DNA.…
We investigate the coefficients generated by expressing the falling factorial $(xy)_k$ as a linear combination of falling factorial products $(x)_l (y)_m$ for $l,m =1,...,k$. Algebraic and combinatoric properties of these coefficients are…
We consider a formulation of Cauchy problem for Kolmogorov equation which corresponds a localized source of particles to be scattered by medium with given scattering amplitude density. The multiple scattering amplitudes are introduced and…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…