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

Abstract

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.

GPU-Based Volume Reconstruction from Very Few Arbitrarily Aligned X-Ray Images

“…Future work will include a thorough evaluation of its performance when compared to Tikhonov regularization or other methods. In fact, further investigation of the few-view limited-angle reconstruction problem will focus on efficient regularization, including statistical approaches based on Bayesian inversion [24,10,11,18]. The capability of the latter to further reduce problem-related reconstruction artifacts has been demonstrated already [10,11,18].…”

“…In many application areas 3D information is desired, although only a severely limited amount of data can be collected. In intraoral imaging or mammograms, for instance, measurements can be obtained only in a very small angular field [26,24,10,11,18,27,30]. Industrial applications such as systems for material examination or luggage inspection usually are made up of an assembly containing only a few projection units in a restricted projection geometry [12].…”

“…To overcome this problem a priori information on the object to be reconstructed can be used. Regularization using total variation or the Besov norm, respectively, are based on object characteristics like smoothness or compactness to generate desirable reconstruction results (see, e.g., [10,20,23]). An eligible framework for obtaining 3D reconstructions in a setting with arbitrary imaging geometry and very few projections is given by the algebraic reconstruction techniques (ART) [16,9].…”

Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques

“…Note that 2 ͑x͒ is the L-1 norm of the gradient, i.e., a total-variation function, which is commonly used as an objective function in many optimization applications to encourage a piecewise constant solution. 19,20 II.C. Search for an optimal solution in a sparse space using a multiobjective optimization…”

A Primal-Dual Active-Set Method for Non-Negativity Constrained Total Variation Deblurring Problems

“…They have proven to be successful in dealing with image denoising and deblurring problems [1], [4]- [6], image inpainting problems [7], and image decomposition [8]. Recently, they have also been applied in various areas such as CT imaging [9], [10] and confocal microscopy [11]. The main advantage of the TV formulation is the ability to preserve edges in the image.…”