Edge-preserving tomographic reconstruction with nonlocal regularization

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.

Polygonal and polyhedral contour reconstruction in computed tomography

This paper is about three-dimensional (3-D) reconstruction of a binary image from its X-ray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonlinear inverse problem using the Bayesian framework. Vertice estimation is done without using a voxel approximation of the 3-D image. It is based on the construction and optimization of a regularized criterion that accounts for surface smoothness. We investigate original deterministic local algorithms, based on the exact computation of the line projections, their update, and their derivatives with respect to the vertice coordinates. Results are first derived in the two-dimensional (2-D) case, which consists of reconstructing a 2-D object of deformable polygonal contour from its tomographic data. Then, we investigate the 3-D extension that requires technical adaptations. Simulation results illustrate the performance of polygonal and polyhedral reconstruction algorithms in terms of quality and computation time.

Statistical inversion for medical x-ray tomography with few radiographs: I. General theory

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.

Tomographic mammography using a limited number of low-dose cone-beam projection images

A method is described for using a limited number (typically 10-50) of low-dose radiographs to reconstruct the three-dimensional (3D) distribution of x-ray attenuation in the breast. The method uses x-ray cone-beam imaging, an electronic digital detector, and constrained nonlinear iterative computational techniques. Images are reconstructed with high resolution in two dimensions and lower resolution in the third dimension. The 3D distribution of attenuation that is projected into one image in conventional mammography can be separated into many layers (typically 30-80 1-mm-thick layers, depending on breast thickness), increasing the conspicuity of features that are often obscured by overlapping structure in a single-projection view. Schemes that record breast images at nonuniform angular increments, nonuniform image exposure, and nonuniform detector resolution are investigated in order to reduce the total x-ray exposure necessary to obtain diagnostically useful 3D reconstructions, and to improve the quality of the reconstructed images for a given exposure. The total patient radiation dose can be comparable to that used for a standard two-view mammogram. The method is illustrated with images from mastectomy specimens, a phantom, and human volunteers. The results show how image quality is affected by various data-collection protocols.