95 research outputs found
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
EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments
We review developments, issues and challenges in Electrical Impedance
Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT,
Manchester 2003. We focus on the necessity for three dimensional data
collection and reconstruction, efficient solution of the forward problem and
present and future reconstruction algorithms. We also suggest common pitfalls
or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of
EIT, Manchester, UK, 200
Three Dimensional Polarimetric Neutron Tomography of Magnetic Fields
Through the use of Time-of-Flight Three Dimensional Polarimetric Neutron
Tomography (ToF 3DPNT) we have for the first time successfully demonstrated a
technique capable of measuring and reconstructing three dimensional magnetic
field strengths and directions unobtrusively and non-destructively with the
potential to probe the interior of bulk samples which is not amenable
otherwise.
Using a pioneering polarimetric set-up for ToF neutron instrumentation in
combination with a newly developed tailored reconstruction algorithm, the
magnetic field generated by a current carrying solenoid has been measured and
reconstructed, thereby providing the proof-of-principle of a technique able to
reveal hitherto unobtainable information on the magnetic fields in the bulk of
materials and devices, due to a high degree of penetration into many materials,
including metals, and the sensitivity of neutron polarisation to magnetic
fields. The technique puts the potential of the ToF time structure of pulsed
neutron sources to full use in order to optimise the recorded information
quality and reduce measurement time.Comment: 12 pages, 4 figure
Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object classification
The early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterisation information. The magnetic polarizability tensor (MPT) offers an economical characterisation of metallic objects and its spectral signature provides additional object characterisation information. The MPT spectral signature can be determined from measurements of the induced voltage over a range frequencies in a metal signature for a hidden object. With classification in mind, it can also be computed in advance for different threat and non-threat objects. In the article, we evaluate the performance of probabilistic and non-probabilistic machine learning algorithms, trained using a dictionary of computed MPT spectral signatures, to classify objects for metal detection. We discuss the importances of using appropriate features and selecting an appropriate algorithm depending on the classification problem being solved and we present numerical results for a range of practically motivated metal detection classification problems
Characterizing the shape and material properties of hidden targets from magnetic induction data
The aim of this paper is to show that, for the eddy current model, the leading order term for the perturbation in the magnetic field, due to the presence of a small conducting magnetic inclusion, can be expressed in terms of a symmetric rank 2 polarization tensor. This tensor contains information about the shape and material properties of the object and is independent of position. We apply a recently derived asymptotic formula for the perturbed magnetic field, due to the presence of a conducting inclusion, which is expressed in terms of a new class of rank 4 polarization tensors (Ammari, H., Chen, J., Chen, Z., Garnier, J. & Volkov, D. (2014) Target detection and characterization from electromagnetic induction data. J. Math. Pures Appl., 101, 54–75.) and show that their result can be written in an alternative form involving a symmetric rank 2 tensor involving 6 instead of 81 complex components in an orthonormal coordinate frame. For objects with rotational and mirror symmetries we show that the number of coefficients is still smaller. We include numerical examples to demonstrate that the new polarization tensors can be accurately computed by solving a vector-valued transmission problem by hp-finite elements and include examples to illustrate the agreement between the asymptotic formula describing the perturbed fields and the numerical predictions
Recovering the second moment of the strain distribution from neutron Bragg edge data
Point by point strain scanning is often used to map the residual stress
(strain) in engineering materials and components. However, the gauge volume and
hence spatial resolution is limited by the beam defining apertures and can be
anisotropic for very low and high diffraction (scattering) angles.
Alternatively, wavelength resolved neutron transmission imaging has a potential
to retrieve information tomographically about residual strain induced within
materials through measurement in transmission of Bragg edges - crystallographic
fingerprints whose locations and shapes depend on microstructure and strain
distribution. In such a case the spatial resolution is determined by the
geometrical blurring of the measurement setup and the detector point spread
function. Mathematically, reconstruction of strain tensor field is described by
the longitudinal ray transform; this transform has a non-trivial null-space,
making direct inversion impossible. A combination of the longitudinal ray
transform with physical constraints was used to reconstruct strain tensor
fields in convex objects. To relax physical constraints and generalise
reconstruction, a recently introduced concept of histogram tomography can be
employed. Histogram tomography relies on our ability to resolve the
distribution of strain in the beam direction, as we discuss in the paper. More
specifically, Bragg edge strain tomography requires extraction of the second
moment (variance about zero) of the strain distribution which has not yet been
demonstrated in practice. In this paper we verify experimentally that the
second moment can be reliably measured for a previously well characterised
aluminium ring and plug sample. We compare experimental measurements against
numerical calculation and further support our conclusions by rigorous
uncertainty quantification of the estimated mean and variance of the strain
distribution
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