On the existence and convergence of the solution of PML equations

In this article we study the mesh termination method in computational scattering theory known as the method of Perfectly Matched Layer (PML). This method is based on the idea of surrounding the scatterer and its immediate vicinity with a fictitious absorbing non-reflecting layer to damp the echoes coming from the mesh termination surface. The method can be formulated equivalently as a complex stretching of the exterior domain. The article is devoted to the existence and convergence questions of the solutions of the resulting equations. We show that with a special choice of the fictitious absorbing coefficient, the PML equations are solvable for all wave numbers, and as the PML layer is made thicker, the PML solution converge exponentially towards the actual scattering solution. The proofs are based on boundary integral methods and a new type of near-field version of the radiation condition, called here the double surface radiation condition. Partly supported by the Finnish Academy, project 37692.     

Modification of E-glass fiber surfaces with polyacrylic acid polymers from an aqueous solution

The research reported in the article focuses on modifying glass fiber surfaces with polyacrylic acid (PAA) compounds. E-glass fibers were treated with aqueous polyacrylic acid solution. Polyacrylic acid exchanges its protons with the ions present in the glass surface. Hydrolyzed metal cations may form salt complexes with the dissociated polyacrylic acid. Angular dependent electron spectroscopy for chemical analysis (ESCA) demonstrated that the atomic concentrations of aluminum and calcium in the glass fiber surface were constant throughout the analyzed interval. The cation exchange property of glass fiber was studied using direct current plasma (DCP), which showed that both calcium and aluminum ions were extracted by low concentration polycrylic acid solutions. ESCA studies of were extracted by low concentrationb polyacrylic acid solutions. ESCA studies of the PAA-treated glass fiber showed that the amount of PAA of the glass surface increases with increased acid concentration. A broadened and shifted ESCA peak of the carbon (0 CO) indicates the formation of salt complexes between the polyacrylic acid and metal ions on the glass surface. Polyacrylie acid was modified by an esterification reaction with glycidyl acrylate (GA) in aqueous solution in order to insert organofuctional groups into the PAA chain.     

Wavelet-based reconstruction for limited-angle X-ray tomography

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.     

Electrical impedance tomography problem with inaccurately known boundary and contact impedances

In electrical impedance tomography (EIT) electric currents are injected into a body with unknown electromagnetic properties through a set of contact electrodes at the boundary of the body. The resulting voltages are measured on the same electrodes and the objective is to reconstruct the unknown conductivity function inside the body based on these data. All the traditional approaches to the reconstruction problem assume that the boundary of the body and the electrode-skin contact impedances are known a priori. However, in clinical experiments one usually lacks the exact knowledge of the boundary and contact impedances, and therefore, approximate model domain and contact impedances have to be used in the image reconstruction. However, it has been noticed that even small errors in the shape of the computation domain or contact impedances can cause large systematic artefacts in the reconstructed images, leading to loss of diagnostically relevant information. In a recent paper (Kolehmainen , 2006), we showed how in the 2-D case the errors induced by the inaccurately known boundary can be eliminated as part of the image reconstruction and introduced a novel method for finding a deformed image of the original isotropic conductivity using the theory of TeichmÜller mappings. In this paper, the theory and reconstruction method are extended to include the estimation of unknown contact impedances. The method is implemented numerically and tested with experimental EIT data. The results show that the systematic errors caused by inaccurately known boundary and contact impedances can efficiently be eliminated by the reconstruction method.      

Infinite Photography: New Mathematical Model for High-Resolution Images

A new mathematical image model is introduced using the photographic process as the starting point. Images are represented as infinite sequences of photons allowing analysis at arbitrarily high resolution and leading to novel computational methods for processing, representation, transmission and storage of images. The resulting space of infinite photographs is proved to have a metric structure and to be intimately connected with bounded Borel measures. Theorems are proved indicating that the imaging power of the photographic process exceeds function spaces in the high resolution limit; this implies in particular that natural photographic images need to be modelled by generalized functions. Furthermore, computational results are presented to illustrate the novel algorithms based on photon sequences. The algorithms include stochastic halftoning, representation of cartoon images with outlines, anti-aliasing, blurring and singularity extraction.     

Wind velocity observation with a CW Doppler radar

We study the problem of gathering information about wind velocity from continuous-wave clear-air Doppler radar measurements. The radar is assumed to be a monostatic fixed-frequency Doppler radar, and the wind velocity as well as the reflectivity are modeled as random fields with statistical parameters depending on the altitude. We seek to reconstruct the hodograph curve of the wind profile, i.e., the projection of the wind velocity profile to the ground plane. We show that under certain assumptions of the wind field, the problem reduces to a well-known problem occurring in classical X-ray tomography. Numerical simulations based on the use of X-ray inversion methods are presented.     

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted /spl lscr//sup 1/ and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.     

The influence of EB-crosslinking on barrier properties of HDPE–mica composites

High-density polyethylene (HDPE) was compounded with untreated and surface-treated mica (10, 20, 40 wt %) and composites were injection-molded. The composites were radiation crosslinked (100, 300, 700 kGy) and hydrocarbon permeability, tensile impact strength, and tensile strength at 25 and 80°C of the composites were examined. The permeability of HDPE decreased from 7 to 3.6 g/(d × m²) by compounding the polymer with 20 wt % mica, and the permeability was additionally reduced to 1.3 g/(d × m²) by irradiation of the compounds (700 kGy). When surface-treated mica was used, the permeability of the composite furthermore decreased to about 1.0 g/(d × m²). Upon irradiation, the E modulus measured at 25°C increased 5% when the dose was 300 kGy. At 80°C, the corresponding increase was 40%. The tensile impact strength of an unfilled polymer increased more than three times by an irradiation dose of 700 kGy, and for a polymer with 10 wt % mica, the tensile impact strength was twice the level of an unirradiated composite. © 1996 John Wiley & Sons, Inc.