3,131 research outputs found
3D particle tracking velocimetry using dynamic discrete tomography
Particle tracking velocimetry in 3D is becoming an increasingly important
imaging tool in the study of fluid dynamics, combustion as well as plasmas. We
introduce a dynamic discrete tomography algorithm for reconstructing particle
trajectories from projections. The algorithm is efficient for data from two
projection directions and exact in the sense that it finds a solution
consistent with the experimental data. Non-uniqueness of solutions can be
detected and solutions can be tracked individually
Histogram Tomography
In many tomographic imaging problems the data consist of integrals along
lines or curves. Increasingly we encounter "rich tomography" problems where the
quantity imaged is higher dimensional than a scalar per voxel, including
vectors tensors and functions. The data can also be higher dimensional and in
many cases consists of a one or two dimensional spectrum for each ray. In many
such cases the data contain not just integrals along rays but the distribution
of values along the ray. If this is discretized into bins we can think of this
as a histogram. In this paper we introduce the concept of "histogram
tomography". For scalar problems with histogram data this holds the possibility
of reconstruction with fewer rays. In vector and tensor problems it holds the
promise of reconstruction of images that are in the null space of related
integral transforms. For scalar histogram tomography problems we show how bins
in the histogram correspond to reconstructing level sets of function, while
moments of the distribution are the x-ray transform of powers of the unknown
function. In the vector case we give a reconstruction procedure for potential
components of the field. We demonstrate how the histogram longitudinal ray
transform data can be extracted from Bragg edge neutron spectral data and
hence, using moments, a non-linear system of partial differential equations
derived for the strain tensor. In x-ray diffraction tomography of strain the
transverse ray transform can be deduced from the diffraction pattern the full
histogram transverse ray transform cannot. We give an explicit example of
distributions of strain along a line that produce the same diffraction pattern,
and characterize the null space of the relevant transform.Comment: Small corrections from last versio
Reconstruction of Residual Stress in a Welded Plate Using the Variational Eigenstrain Approach
We present the formulation for finding the distribution of eigenstrains, i.e.
the sources of residual stress, from a set of measurements of residual elastic
strain (e.g. by diffraction), or residual stress, or stress redistribution, or
distortion. The variational formulation employed seeks to achieve the best
agreement between the model prediction and some measured parameters in the
sense of a minimum of a functional given by a sum over the entire set of
measurements. The advantage of this approach lies in its flexibility: different
sets of measurements and information about different components of the
stress-strain state can be incorporated. We demonstrate the power of the
technique by analysing experimental data for welds in thin sheet of a nickel
superalloy aerospace material. Very good agreement can be achieved between the
prediction and the measurement results without the necessity of using iterative
solution. In practice complete characterisation of residual stress states is
often very difficult, due to limitations of facility access, measurement time
or specimen dimensions. Implications of the new technique for experimental
analysis are all the more significant, since it allows the reconstruction of
the entire stress state from incomplete sets of data.Comment: 16 pages, 17 figure
Network Flow Algorithms for Discrete Tomography
Tomography is a powerful technique to obtain images of the interior of an object in a nondestructive way. First, a series of projection images (e.g., X-ray images) is acquired and subsequently a reconstruction of the interior is computed from the available project data. The algorithms that are used to compute such reconstructions are known as tomographic reconstruction algorithms. Discrete tomography is concerned with the tomographic reconstruction of images that are known to contain only a few different gray levels. By using this knowledge in the reconstruction algorithm it is often possible to reduce the number of projections required to compute an accurate reconstruction, compared to algorithms that do not use prior knowledge. This thesis deals with new reconstruction algorithms for discrete tomography. In particular, the first five chapters are about reconstruction algorithms based on network flow methods. These algorithms make use of an elegant correspondence between certain types of tomography problems and network flow problems from the field of Operations Research. Chapter 6 deals with a problem that occurs in the application of discrete tomography to the reconstruction of nanocrystals from projections obtained by electron microscopy.The research for this thesis has been financially supported by the Netherlands Organisation for Scientific Research (NWO), project 613.000.112.UBL - phd migration 201
On the Reconstruction of Static and Dynamic Discrete Structures
We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in ). The main emphasis is on recent mathematical developments and new applications, which emerge in scientific areas such as physics and materials science, but also in inner mathematical fields such as number theory, optimization, and imaging. Along with a concise introduction to the field of discrete tomography, we give pointers to related aspects of computerized tomography in order to contrast the worlds of continuous and discrete inverse problems
An Algebraic Framework for Discrete Tomography: Revealing the Structure of Dependencies
Discrete tomography is concerned with the reconstruction of images that are
defined on a discrete set of lattice points from their projections in several
directions. The range of values that can be assigned to each lattice point is
typically a small discrete set. In this paper we present a framework for
studying these problems from an algebraic perspective, based on Ring Theory and
Commutative Algebra. A principal advantage of this abstract setting is that a
vast body of existing theory becomes accessible for solving Discrete Tomography
problems. We provide proofs of several new results on the structure of
dependencies between projections, including a discrete analogon of the
well-known Helgason-Ludwig consistency conditions from continuous tomography.Comment: 20 pages, 1 figure, updated to reflect reader inpu
Muon Track Reconstruction and Data Selection Techniques in AMANDA
The Antarctic Muon And Neutrino Detector Array (AMANDA) is a high-energy
neutrino telescope operating at the geographic South Pole. It is a lattice of
photo-multiplier tubes buried deep in the polar ice between 1500m and 2000m.
The primary goal of this detector is to discover astrophysical sources of high
energy neutrinos. A high-energy muon neutrino coming through the earth from the
Northern Hemisphere can be identified by the secondary muon moving upward
through the detector. The muon tracks are reconstructed with a maximum
likelihood method. It models the arrival times and amplitudes of Cherenkov
photons registered by the photo-multipliers. This paper describes the different
methods of reconstruction, which have been successfully implemented within
AMANDA. Strategies for optimizing the reconstruction performance and rejecting
background are presented. For a typical analysis procedure the direction of
tracks are reconstructed with about 2 degree accuracy.Comment: 40 pages, 16 Postscript figures, uses elsart.st
- âŠ