The field of discrete tomography focuses on the reconstruction of samples that consist of only a few different materials. Ideally, a 3D reconstruction of such a sample should contain only one grey level for each of the compositions in the sample. By exploiting this property in the reconstruction algorithm, either the quality of the reconstruction can be improved significantly, or the number of ...

Basic properties of finite subsets of the integer lattice Z are investigated from the point of view of geometric tomography. Results obtained concern the Minkowski addition of convex lattice sets and polyominoes, discrete X-rays and the discrete and continuous covariogram, the determination of symmetric convex lattice sets from the cardinality of their projections on hyperplanes, and a discrete...

We study different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g. to perform full tomography of this state. We focus on two apparently simple cases, full tomography of one and two qubit systems. We analyze and compare those techniques according to two figures of merit. Our first criterion is the minimisation of the redundancy of the data acquired during...

Abstract Reconstructing a discrete object by means of X-rays along finite set U (discrete) directions represents one the main task in tomography. Indeed, it is an ill-posed inverse problem, since different structures exist having same projections all lines whose range . Characteristic ambiguous reconstructions are special configurations, called switching components, understanding issue tomograp...

In November of 2005 a measurement series was conducted on different kinds of reference objects to compare the results of the FRM-II (ANTARES) and the Budapest (Radiography Station) research reactor in the field of neutron radiography, gamma radiography, classical tomography and discrete tomography by an ANDOR CCD camera and Imaging plate with BAS 2500 Scanner (contributed by AIDA software).

Projective computer tomography and image reconstruction of discrete structure of materials Computer tomography is efficiently used in different applied areas, particularly for investigation of the material's structure. Traditional approach requires scanning the object with a lot of angles and reconstruction of images, using sufficiently difficult mathematical operations as, for example, the inv...

Filling operations are procedures which are used in Discrete Tomography for the reconstruction of lattice sets having some convexity constraints. Many algorithms have been published giving fast implementations of these operations, and the best running time ([7]) is O(N2 log N) time, where N is the size of projections. In this paper we improve this result by providing an implementation of the fi...

We study the problem of scheduling multiple sensors to visit and observe a group of sites at discrete time points over a planning horizon of given length. We show that scheduling under a given number of visits for each site and in each period is an NP-complete problem by providing equivalence with a problem in discrete tomography. We also give a polynomial time algorithm to schedule the sensors...

A new kind of discrete tomography problem is introduced: the reconstruction of discrete sets from their absorbed projections. A special case of this problem is discussed, namely, the uniqueness of the binary matrices with respect to their absorbed row and column sums when the absorption coefficient is = log((1+√5)/2). It is proved that if a binary matrix contains a special structure of 0s and 1...

We address a discrete tomography problem that arises in the study of the atomic structure of crystal lattices. A polyatomic structure T can be defined as an integer lattice in dimension D ≥ 2, whose points may be occupied by c distinct types of atoms. To “analyze” T , we conduct l measurements that we call discrete X-rays. A discrete X-ray in direction ξ determines the number of atoms of each t...