Comparison between a time-domain and a frequency-domain system for optical tomography.

The quality of phase and amplitude data from two medical optical tomography systems were compared. The two systems are a 32-channel time-domain system developed at University College London (UCL) and a 16-channel frequency-domain system developed at Helsinki University of Technology (HUT). Difference data measured from an inhomogeneous and a homogeneous phantom were compared with a finite-element method (diffusion equation) and images of scattering and absorption were reconstructed based on it. The measurements were performed at measurement times between 1 and 30 s per source. The mean rms errors in the data measured by the HUT system were 3.4% for amplitude and 0.51 deg for phase, while the corresponding values for the UCL data were 6.0% and 0.46 deg, respectively. The reproducibility of the data measured with the two systems was tested with a measurement time of 5 s per source. It was 0.4% in amplitude for the HUT system and 4% for the UCL system, and 0.08 deg in phase for both systems. The image quality of the reconstructions from the data measured with the two systems were compared with several quantitative criteria. In general a higher contrast was observed in the images calculated from the HUT data.

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.

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 l1 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.

Representation of bioelectric current sources using Whitney elements in the finite element method.

Bioelectric current sources of magneto- and electroencephalograms (MEG, EEG) are usually modelled with discrete delta-function type current dipoles, despite the fact that the currents in the brain are naturally continuous throughout the neuronal tissue. In this study, we represent bioelectric current sources in terms of Whitney-type elements in the finite element method (FEM) using a tetrahedral mesh. The aim is to study how well the Whitney elements can reproduce the potential and magnetic field patterns generated by a point current dipole in a homogeneous conducting sphere. The electric potential is solved for a unit sphere model with isotropic conductivity and magnetic fields are calculated for points located on a cap outside the sphere. The computed potential and magnetic field are compared with analytical solutions for a current dipole. Relative difference measures between the FEM and analytical solutions are less than 1%, suggesting that Whitney elements as bioelectric current sources are able to produce the same potential and magnetic field patterns as the point dipole sources.

Modeling anisotropic light propagation in a realistic model of the human head.

A Monte Carlo model capable of describing photon migration in arbitrary three-dimensional geometry with spatially varying optical properties and tissue anisotropy is presented. We use the model to explore the effects of anisotropy for optical measurements of the human head. An anisotropic diffusion equation that corresponds to our Monte Carlo model is derived, and a comparison between the Monte Carlo model and the diffusion equation solution with finite elements is given.