Related papers: On discrete X-ray transform

We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the…

Conventional X-ray methods use incoming plane waves and result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered…

We study a class of multiplicative algorithms introduced by Silvey et al. (1978) for computing D-optimal designs. Strict monotonicity is established for a variant considered by Titterington (1978). A formula for the rate of convergence is…

Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional…

In this paper, we introduce a discrete Riesz transforms associated with the non-symmetric trigonometric Heckman-Opdam polynomials of type $A_1$. We prove that they can be extended to a bounded operators on $\ell^p(\mathbb{Z})$,…

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…

We introduce a revised de Broglie relation in discrete space-time, and analyze some possible inferences of the relation.

In this paper, we present XctDiff, an algorithm framework for reconstructing CT from a single radiograph, which decomposes the reconstruction process into two easily controllable tasks: feature extraction and CT reconstruction.…

We continue our investigation of Discrete Riemann Surfaces with the discussion of the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument, series and electrical moves. We show that given a…

We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…

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.…

In this paper, we introduce the n-th discrete topological complexity and study its properties such as its relation with simplicial Lusternik-Schnirelmann category and how the higher dimensions of discrete topological complexity relate with…

We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms.…

A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the…

We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider…

Image processing is an increasingly important aspect for analysis of data from X and $\gamma$-ray astrophysics missions. In this paper, I review a method proposed by Kebede (L. W. Kebede 1994, ApJ, 423, 878), and point out an error in the…

I present a brief up-to-date review of the current understanding of Supergiant Fast X-ray Transients, with an emphasis on the observational point of view. After more than a decade since their discovery, a remarkable progress has been made…

Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical…

We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any…

Scanning transmission X-ray microscopy and ptychography have become mature tools for high-resolution, element-specific imaging of nanoscale structures. However, transmission geometries impose stringent constraints on sample thickness and…