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

Comparing D-Bar and Common Regularization-Based Methods for Electrical Impedance Tomography

Objective: To compare D-bar difference reconstruction with regularized linear reconstruction in electrical impedance tomography. Approach: A standard regularized linear approach using a Laplacian penalty and the GREIT method for comparison to the D-bar difference images. Simulated data was generated using a circular phantom with small objects, as well as a \u27Pac-Man\u27 shaped conductivity target. An L-curve method was used for parameter selection in both D-bar and the regularized methods. Main results: We found that the D-bar method had a more position independent point spread function, was less sensitive to errors in electrode position and behaved differently with respect to additive noise than the regularized methods. Significance: The results allow a novel pathway between traditional and D-bar algorithm comparison

The Impact Of Simulated Microgravity On The Growth Of The Model Legume Plant Medicago Truncatula

Simulated microgravity has been a useful tool to help understand plant development in altered gravity conditions. Thirty-one genotypes of the legume plant Medicago truncatula were grown in either simulated microgravity on a rotating clinostat, or a static, vertical environment. Twenty morphological features were measured and compared between these two gravity treatments. Within-species genotypic variation was a significant predictor of the phenotypic response to gravity treatment in 100% of the measured morphological and growth features. In addition, there was a genotype–environment interaction (G×E) for 45% of the response variables, including shoot relative growth rate (p \u3c 0.0005), median number of roots (p ∼ 0.02), and root dry mass (p \u3c 0.005). These findings are discussed in the context of improving future studies in plants space biology by controlling for genotypic differences, and by connecting traits to their underlying genetic causes by using genome-wide association (GWA) mapping. In the long-term, manipulation of genotype effects, in combination with M. truncatula’s symbiotic relationships with rhizobacteria and arbuscular mycorrhizal fungi, will be important for optimizing legumes for cultivation on long-term space missions

Combining Iterative Absolute EIT, Difference EIT and Control Theory to Optimise Mechanical Ventilation

We examine the combination of absolute and difference imaging to provide fast pseudo-absolute EIT reconstructions required for the recovery of local ventilation parameters. Parameters recovered from simulations are incorporated into an optimal control framework to demonstrate personalised optimisation of mechanical ventilation

Does electro-sensing fish use the first order polarization tensor for object characterization? object discrimination test

This paper extends the previous works to further explore the role of the first order polarization tensor in electro-sensing by the weakly electric fish specifically for object discrimination and characterization. The first order polarization tensor for few objects used in the considered experiment are calculated and discussed to identify whether there are other evidences to suggest that a weakly electric fish able to recognize the tensor when choosing or rejecting an object. Our findings in this study suggest that all fish during most of the experiments face difficulties to discriminate two objects when their first order polarization tensors are almost similar depending on the types of training given to them

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