The perturbation of electromagnetic fields at distances that are large compared with the object's size

Abstract We rigorously derive the leading-order terms in asymptotic expansions for the scattered electric and magnetic fields in the presence of a small object at distances that are large compared with its size. Our expansions hold for fixed wavenumber when the scatterer is a (lossy) homogeneous dielectric object with constant material parameters or a perfect conductor. We also derive the corresponding leading-order terms in expansions for the fields for a low-frequency problem when the scatterer is a non-lossy homogeneous dielectric object with constant material parameters or a perfect conductor. In each case, we express our results in terms of polarization tensors.</jats:p

Effect of sparsity and exposure on total variation regularized X-ray tomography from few projections

We address effects of exposure and image gradient sparsity for total variation-regularized reconstruction: is it better to collect many low-quality or few high-quality projections, and can gradient sparsity predict how many projections are necessary? Preliminary results suggest collecting many low-quality projections is favorable, and that a link may exist between gradient sparsity level and successful reconstruction

Reconstruction Algorithms for Permittivity and Conductivity Imaging

Linear reconstruction algorithms are reviewed using assumed covariance matrices for the conductivity and data and the formulation of Tikhonov regularization using the singular value decomposition (SVD) with covariance norms. It is shown how iterative reconstruction algorithms, such as Landweber and conjugate gradient, can be used for regularization and analysed in terms of the SVD, and implemented directly for a one−step Newton’s method. Where there are known inequality constraints, such as upper and lower bounds, these can be incorporated in iterative methods and have a stabilizing effect on reconstructions

Notes on Histotomography

In many tomographic imaging problems the data consists of integrals along lines or curves. Increas- ingly we are seeing “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 contains 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 talk we introduce the concept of “histotomogra- phy”. 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. We will illustrate with examples from scalar spectral attenuation tomography and tensor tomography methods for strain using neutrons, electrons and x-rays

Boundary Shape and Electrical Impedance Tomography

In electrical impedance tomography the boundary shape is often inaccurately known. If the boundary shape is wrong (in a three-dimensional problem) there will not generally be an isotropic conductivity which fits the current and voltage data. Both the conductivity and boundary shape can be determined by electrical data together with three spatial measurements. In two dimensions errors in boundary shape could be accounted for by a change in conductivity, but not if the length scale on the boundary is also known

An MRI DICOM data set of the head of a normal male human aged 52

<p>This zip file contains a DICOM data set of magnetic resonance images  a normal male mathematics professor aged 52. The experimental subject is the author. The MRI scans are T2 weighted  turbo-spin-echo (T2W TSE) and T1 weighted Fast Field Echo (T1W FFE).</p> <p>The subject suffers from a small vertical strabismus (hypertropia), a misalignment of the eyes, which is visible in this data set.</p> <p>The author would like to thank the Radiology Department at the Macclesfield General Hospital for performing the scan.</p> <p> </p

The SVD of the linearized EIT problem on a disk

Abstract: In this paper we calculate the right singular functions to the linearized EIT problem on homogeneous disk. We note the similarity to Zernike disk functions and the dependence on the mesh

Conductivity perturbations in EIT

Difference EIT reconstructs a signal generated by conductivity contrasting regions. We explore the effect that, for large contrasts, conductive regions produce a greater signal than non-conductive ones, and this difference is determined by the region shap

Adjoint Formulations in Impedance Imaging

Most reconstruction algorithms in electrical impedance tomography (EIT, ERT and ECT) are known to suffer from the computational costs of calculating the Jacobian (also known as sensitivity matrix). In this paper we review and slightly modify the adjoint fields technique already widely used in electromagnetic imaging, diffuse optical and ultrasound tomography, which enables the reconstruction of nonlinear solutions without the explicit calculation of the Jacobian. This has enormous computational advantages in the efficiency of image reconstruction. Here we address the complex isotropic EIT problem

Bistatic two dimensional synthetic aperture radar as a tensor tomography problem

Bistatic radar uses a separate location for the transmitter and receiver, for example on two aircraft or UAVs. The transmitter sends out a pulse and the receiver records its magnitude, for each travel time (we consider the incoherent case, most systems in practice record also the phase). For each transmitter and receiver position a measurement at a given travel time is the sum of reflections on a prolate spheroid (ellipse in two dimensional case) with the transmitter and receiver as its foci. If the transmitter and receiver are distant from reflectors supported in a small ball the spheroids can be approximated by planes. Although reflectors are commonly assumed to be isotropic, in practice the relative amplitude of reflection depends on the incoming and outgoing direction, described by the (bistatic) radar scattering cross-section. In this poster we relate this problem to a tensor Radon transform, which in two dimensions has an explicit singular value decomposition