Edge-promoting reconstruction of absorption and diffusivity in optical tomography

In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption and diffusivity. In this work, it is assumed that the imaged object is composed of an approximately homogeneous background with clearly distinguishable embedded inhomogeneities. An algorithm for finding the maximum a posteriori estimate for the absorption and diffusion coefficients is introduced assuming an edge-preferring prior and an additive Gaussian measurement noise model. The method is based on iteratively combining a lagged diffusivity step and a linearization of the measurement model of diffuse optical tomography with priorconditioned LSQR. The performance of the reconstruction technique is tested via three-dimensional numerical experiments with simulated measurement data.Comment: 18 pages, 6 figure

Computational framework for applying electrical impedance tomography to head imaging

This work introduces a computational framework for applying absolute electrical impedance tomography to head imaging without accurate information on the head shape or the electrode positions. A library of fifty heads is employed to build a principal component model for the typical variations in the shape of the human head, which leads to a relatively accurate parametrization for head shapes with only a few free parameters. The estimation of these shape parameters and the electrode positions is incorporated in a regularized Newton-type output least squares reconstruction algorithm. The presented numerical experiments demonstrate that strong enough variations in the internal conductivity of a human head can be detected by absolute electrical impedance tomography even if the geometric information on the measurement configuration is incomplete to an extent that is to be expected in practice.Comment: 25 pages, 12 figure

Inverse heat source problem and experimental design for determining iron loss distribution

Iron loss determination in the magnetic core of an electrical machine, such as a motor or a transformer, is formulated as an inverse heat source problem. The sensor positions inside the object are optimized in order to minimize the uncertainty in the reconstruction in the sense of the A-optimality of Bayesian experimental design. This paper focuses on the problem formulation and an efficient numerical solution of the discretized sensor optimization and source reconstruction problems. A semirealistic linear model is discretized by finite elements and studied numerically.Comment: 30 pages, 15 figure

Distributed solution of Laplacian eigenvalue problems

The purpose of this article is to approximately compute the eigenvalues of the symmetric Dirichlet Laplacian within an interval $(0,\Lambda)$. A novel domain decomposition Ritz method, partition of unity condensed pole interpolation method, is proposed. This method can be used in distributed computing environments where communication is expensive, e.g., in clusters running on cloud computing services or networked workstations. The Ritz space is obtained from local subspaces consistent with a decomposition of the domain into subdomains. These local subspaces are constructed independently of each other, using data only related to the corresponding subdomain. Relative eigenvalue error is analysed. Numerical examples on a cluster of workstations validate the error analysis and the performance of the method.Comment: 28 page