[1] In this paper, formulation of the surface integral equations for solving electromagnetic scattering by dielectric and composite metallic and dielectric objects with iterative methods is studied. Four types of formulations are considered: T formulations, N formulations, the combined field integral equation formulation, and the Müller formulation. By studying properties of the integral equations and their testing in the Galerkin method, ''optimal'' forms for each formulation type are derived. Numerical examples demonstrate that the developed new formulations lead to clear improvements in the convergence rates when the matrix equations are solved iteratively with the generalized minimal residual method. Both the Rao-Wilton-Glisson and Trintinalia-Ling (TL) basis functions are used in expanding the unknown electric and magnetic surface current densities. In particular, the first-order TL basis functions are required in the N formulations to maintain the solution accuracy when the surfaces include sharp edges.Citation: Ylä-Oijala, P., M. Taskinen, and S. Järvenpää (2005), Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods, Radio Sci., 40, RS6002,

In x-ray tomography, the structure of a three-dimensional body is reconstructed from a collection of projection images of the body. Medical CT imaging does this using an extensive set of projections from all around the body. However, in many practical imaging situations only a small number of truncated projections are available from a limited angle of view. Three-dimensional imaging using such data is complicated for two reasons: (i) typically, sparse projection data do not contain sufficient information to completely describe the 3D body, and (ii) traditional CT reconstruction algorithms, such as filtered backprojection, do not work well when applied to few irregularly spaced projections. Concerning (i), existing results about the information content of sparse projection data are reviewed and discussed. Concerning (ii), it is shown how Bayesian inversion methods can be used to incorporate a priori information into the reconstruction method, leading to improved image quality over traditional methods. Based on the discussion, a low-dose three-dimensional x-ray imaging modality is described.

The aim of X-ray tomography is to reconstruct an unknown physical body from a collection of projection images. When the projection images are only available from a limited angle of view, the reconstruction problem is a severely ill-posed inverse problem. Statistical inversion allows stable solution of the limited-angle tomography problem by complementing the measurement data by a priori information. In this work, the unknown attenuation distribution inside the body is represented as a wavelet expansion, and a Besov space prior distribution together with positivity constraint is used. The wavelet expansion is thresholded before reconstruction to reduce the dimension of the computational problem. Feasibility of the method is demonstrated by numerical examples using in vitro data from mammography and dental radiology.

This article presents results of a numerical effort to determine the dielectric polarizabilities of the five regular polyhedra: tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The polarizability is calculated by solving a surface integral equation, in which the unknown potential is expanded using third-order basis functions. The resulting polarizabilities are accurate to the order of 10 4 . Approximation formulas are given for the polarizabilities as functions of permittivity. Among other results, it is found that the polarizability of a regular polyhedron correlates more strongly with the number of edges than with the number of faces, vertices, or the solid angle seen from a vertex.Index Terms-High-order basis functions, polarizability, polyhedra, surface integral equation.

Diagnostic and operational tasks in dental radiology often require three-dimensional information that is difficult or impossible to see in a projection image. A CT-scan provides the dentist with comprehensive three-dimensional data. However, often CT-scan is impractical and, instead, only a few projection radiographs with sparsely distributed projection directions are available. Statistical (Bayesian) inversion is well-suited approach for reconstruction from such incomplete data. In statistical inversion, a priori information is used to compensate for the incomplete information of the data. The inverse problem is recast in the form of statistical inference from the posterior probability distribution that is based on statistical models of the projection data and the a priori information of the tissue. In this paper, a statistical model for three-dimensional imaging of dentomaxillofacial structures is proposed. Optimization and MCMC algorithms are implemented for the computation of posterior statistics. Results are given with in vitro projection data that were taken with a commercial intraoral x-ray sensor. Examples include limited-angle tomography and full-angle tomography with sparse projection data. Reconstructions with traditional tomographic reconstruction methods are given as reference for the assessment of the estimates that are based on the statistical model.