Efficient non-linear 3D electrical tomography reconstruction

Non-linear electrical tomography imaging can be performed efficiently if certain optimisations are applied to the computational reconstruction process. We present a 3D non-linear reconstruction algorithm based on a regularized conjugate gradient solver and discuss the optimisations which we incorporated to allow for an efficient and accurate reconstruction. In particular, the application of image smoothness constraints or other regularization techniques and auto-adaptive mesh refinement are highly relevant. We demonstrate the results of applying this algorithm to the reconstruction of a simulated material distribution in a cubic volume

Optimal finite element modelling and efficient reconstruction in non-linear 3D electrical resistance tomography

Electrical Impedance Tomography can provide images with well-defined characteristics using a fully non-linear reconstruction process when appropriate constraints are imposed on the solution to allow the ill-posed inverse problem to be solved. Using appropriate finite element discretizations for forward solution and inverse problem offers additional advantages in the image reconstruction process, such as (a) inclusion of prior knowledge, (b) generic model templating to adapt to, for example, individual head shapes, and (c) obtaining accurate results without unnecessary computational overhead. We have developed an efficient 3D non-linear reconstruction algorithm based on a regularized inverse conjugate gradient solver which incorporates (a) local image smoothness constraints, and (b) a number of optimisations which reduce the computing power required to obtain an accurate solution. We show results from applying this to various problems which arise in medical resistivity reconstruction given only surface potential measurements and demonstrate the importance of the FE discretization. Keywords: 3D non-linear electrical impedance tomography, FE template modelling, optimal finite element meshes, 3D visualization, FE discretization

Efficient non-linear 3D electrical tomography and finite element optimizations for functional source imaging

An essential factor in functional source imaging is the accurate knowledge of the conducitvity dostribution inside the body. Current models for electrophysiological forward and inverse problems use tabulated conductivity values obtained from experiments. This article shows how EIT-derived conductivities can be used in EEG reconstructions of a head slice

Terahertz emission by diffusion of carriers and metal-mask dipole inhibition of radiation

Terahertz (THz) radiation can be generated by ultrafast photo-excitation of carriers in a semiconductor partly masked by a gold surface. A simulation of the effect taking into account the diffusion of carriers and the electric field shows that the total net current is approximately zero and cannot account for the THz radiation. Finite element modelling and analytic calculations indicate that the THz emission arises because the metal inhibits the radiation from part of the dipole population, thus creating an asymmetry and therefore a net current. Experimental investigations confirm the simulations and show that metal-mask dipole inhibition can be used to create THz emitters.Comment: 9 pages, 5 figures; Fixed figure

Maximum Entropy, Parallel Computations and Lotteries

By picking unpopular sets of numbers in a lottery, it is possible to increase one’s expected winnings. We have used the Maximum Entropy method to estimate the probability of each of the 14 million tickets being chosen by players in the UK National Lottery. We discuss the parallel solution of the non-linear system of equations on a variety of platforms and give results which indicate the returns achieved by a syndicate buying a large number of tickets each week

Using Maximum Entropy to Double One's Expected Winnings in the UK National Lottery 1998

We have used the Maximum Entropy method to estimate the probability of each of the 14 million tickets being chosen by players in the UK National Lottery. As data, we used the numbers of winners in the 3, 4, and 5-match categories and the total number of tickets sold in each of the first 113 draws. We have computed the marginal distributions for players choosing single numbers and pairs of numbers. A striking conclusion is that players preferentially pick numbers towards the centre of the ticket. By choosing unpopular combinations of numbers, one's expected winnings can be doubled

Non-linear electrical tomography reconstruction of simple test objects and a simulated head slice

Fully non-linear reconstruction in Electrical Tomography produces images with well-defined characteristics when explicit guides are imposed on the accessible solutions. In this paper, we revisit the formulation of the problem and apply the algorithm to some simulated test objects, and to a simple 2-dimensional model of the human head. The results demonstrate the best fidelity of reconstruction which may be achieved with existing and potentially attainable levels of signal to noise. We use a finite element model with some adaptive capability so that the images generated by the chosen constraint are not perturbed by the coarseness of the mesh. The algorithm incorporates a number of optimisations to reduce the required computing power and storage space, these include:Sparse matrix storage scheme and optimised sparse numerical handlingProblem-adapted element shape and densityUsage of high quality finite element meshesPre-evaluation of used quantities and matrices and application of numerical techniques such as the Woodbury formul

Pyroelectric field assisted ion migration induced by ultraviolet laser irradiation and its impact on ferroelectric domain inversion in lithium niobate crystals

The impact of UV laser irradiation on the distribution of lithium ions in ferroelectric lithium niobate single crystals has been numerically modelled. Strongly absorbed UV radiation at wavelengths of 244–305nm produces steep temperature gradients which cause lithium ions to migrate and result in a local variation of the lithium concentration. In addition to the diffusion, here the pyroelectric effect is also taken into account which predicts a complex distribution of lithium concentration along the c-axis of the crystal: two separated lithium deficient regions on the surface and in depth. The modelling on the local lithium concentration and the subsequent variation of the coercive field are used to explain experimental results on the domain inversion of such UV treated lithium niobate crystals

Prospects for high fidelity imaging in nonlinear EIT using high performance computing

Linear image reconstruction in EIT has been widely used in medical and process applications, and nearly all of these have been based on approximately uniform distributions of the electrical conductivity in the object under study. Successful applications in medicine have been reported although the markedly non-uniform conductivity distribution in the human body, which is not known a priori, means that artefacts produced by the linear imaging approximation are difficult to exclude. It is important therefore to pursue the full nonlinear problem in order to provide a firm basis for subsequent linear treatments; we have already shown that effective nonlinear EIT can be achieved when appropriate choices are made to constrain the form of the images sought [Blott et al 1998]. In this paper we explore the image resolutions potentially achievable with the availability of improved signal-to-noise in the data. The advent of modern high performance computing allows the production of accurate reference images in practicable time scales, and these can then be used as the basis of high fidelity linear imaging systems in real-time applications. In addition, it becomes feasible to tackle the full 3-d problem