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Bayesian inversion method for 3d dental xray imaging
 Elektrotechnik & Informationstechnik
"... Abstract Diagnostic and operational tasks in dentistry require threedimensional (3D) information about tissue. A novel type of low dose dental 3D Xray imaging is considered. Given projection images taken from a few sparsely distributed directions using the dentist’s regular Xray equipment, the ..."
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Abstract Diagnostic and operational tasks in dentistry require threedimensional (3D) information about tissue. A novel type of low dose dental 3D Xray imaging is considered. Given projection images taken from a few sparsely distributed directions using the dentist’s regular Xray equipment, the 3D Xray attenuation function is reconstructed. This is an illposed inverse problem, and Bayesian inversion is a well suited framework for reconstruction from such incomplete data. The reconstruction problem is formulated in a wellposed probabilistic form in which a priori information is used to compensate for the incomplete data. A parallelized Bayesian method (implemented for a Beowulf cluster computer) for 3D reconstruction in dental radiology is presented (the method was originally presented in (Kolehmainen et al., 2006)). The prior model for dental structures consist of a weighted `1 and total variation (TV)prior together with the positivity prior. The inverse problem is stated as nding the maximum a posterior (MAP) estimate. The method is tested with in vivo patient data and shown to outperform the reference method (tomosynthesis).
Waveletbased reconstruction for limitedangle Xray tomography
"... Abstract — The aim of Xray 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 illposed inverse problem. Statistical inversion allows stabl ..."
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Abstract — The aim of Xray 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 illposed inverse problem. Statistical inversion allows stable solution of the limitedangle 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. I.
SPARSE REPRESENTATIONS FOR LIMITED DATA TOMOGRAPHY
, 2007
"... In limited data tomography, with applications such as electron microscopy and medical imaging, the scanning views are within an angular range that is often both limited and sparsely sampled. In these situations, standard algorithms produce reconstructions with notorious artifacts. We show in this pa ..."
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In limited data tomography, with applications such as electron microscopy and medical imaging, the scanning views are within an angular range that is often both limited and sparsely sampled. In these situations, standard algorithms produce reconstructions with notorious artifacts. We show in this paper that a sparsity image representation principle, based on learning dictionaries for sparse representations of image patches, leads to significantly improved reconstructions of the unknown density from its limited angle projections. The presentation of the underlying framework is complemented with illustrative results on artificial and real data.
Limited data Xray tomography using nonlinear evolution equations
 SIAM J. Sci. Comput
"... Abstract. A novel approach to the Xray tomography problem with sparse projection data is proposed. Nonnegativity of the Xray attenuation coefficient is enforced by modelling it as max{Φ(x), 0} where Φ is a smooth function. The function Φ is computed as the equilibrium solution of a nonlinear evo ..."
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Abstract. A novel approach to the Xray tomography problem with sparse projection data is proposed. Nonnegativity of the Xray attenuation coefficient is enforced by modelling it as max{Φ(x), 0} where Φ is a smooth function. The function Φ is computed as the equilibrium solution of a nonlinear evolution equation analogous to the equations used in level set methods. The reconstruction algorithm is applied to (a) simulated full and limited angle projection data of the SheppLogan phantom with sparse angular sampling and (b) measured limited angle projection data of in vitro dental specimens. The results are significantly better than those given by traditional backprojectionbased approaches, and similar in quality (but faster to compute) compared to Algebraic Reconstruction Technique (ART). Key words. Limited angle tomography, Xray tomography, level set, nonlinear evolution equa
2010. A new framework for sparse regularization in limited angle xray tomography
 Biomedical Imaging: From Nano to Macro, 2010 IEEE International Symposium on
"... Abstract We propose a new framework for limited angle tomographic reconstruction. Our approach is based on the observation that for a given acquisition geometry only a few (visible) structures of the object can be reconstructed reliably using a limited angle data set. By formulating this problem in ..."
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Abstract We propose a new framework for limited angle tomographic reconstruction. Our approach is based on the observation that for a given acquisition geometry only a few (visible) structures of the object can be reconstructed reliably using a limited angle data set. By formulating this problem in the curvelet domain, we can characterize those curvelet coefficients which correspond to visible structures in the image domain. The integration of this information into the formulation of the reconstruction problem leads to a considerable dimensionality reduction and yields a speedup of the corresponding reconstruction algorithms.
Statistical Xray tomography using empirical Besov priors
 ADAPTIVE REGULARIZATION FOR TOMOGRAPHY 21
"... Waveletbased Besov space prior models for Xray tomography are studied using the empirical Bayes approach. The hyperparameters for the prior models are estimated from statistical properties of the wavelet coefficients of measured Xray projection images (which are related to the smoothness of the a ..."
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Waveletbased Besov space prior models for Xray tomography are studied using the empirical Bayes approach. The hyperparameters for the prior models are estimated from statistical properties of the wavelet coefficients of measured Xray projection images (which are related to the smoothness of the attenuation coefficient). Various statistical models for the wavelet coefficients are studied. Experiments using measured in vitro data suggest that the hyperparameters can be estimated with a simple method, leading to automated choice of prior parameters and improved tomographic reconstruction.
Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in highdimensional inverse problems using L1type priors
"... Abstract. Sparsity has become a key concept for solving of highdimensional inverse problems using variational regularization techniques. Recently, using similar sparsityconstraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Im ..."
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Abstract. Sparsity has become a key concept for solving of highdimensional inverse problems using variational regularization techniques. Recently, using similar sparsityconstraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Important questions about the relation between regularization theory and Bayesian inference still need to be addressed when using sparsity promoting inversion. A practical obstacle for these examinations is the lack of fast posterior sampling algorithms for sparse, highdimensional Bayesian inversion: Accessing the full range of Bayesian inference methods requires being able to draw samples from the posterior probability distribution in a fast and efficient way. This is usually done using Markov chain Monte Carlo (MCMC) sampling algorithms. In this article, we develop and examine a new implementation of a single component Gibbs MCMC sampler for sparse priors relying on L1norms. We demonstrate that the efficiency of our Gibbs sampler increases when the level of sparsity or the dimension of the unknowns is increased. This property is contrary to the properties of the most commonly applied MetropolisHastings (MH) sampling schemes: We demonstrate that the efficiency of MH schemes for L1type priors dramatically decreases when the level of sparsity or the dimension of the unknowns is increased. Practically, Bayesian inversion for L1type priors using MH samplers is not feasible at all. As this is commonly believed to be an intrinsic feature of MCMC sampling, the performance of our Gibbs sampler also challenges common beliefs about the applicability of sample based Bayesian inference. AMS classification scheme numbers: 65J22,62F15,65C05,65C60
A parametric levelset approach to simultaneous object identification and background reconstruction for dualenergy computed tomography
 Image Processing, IEEE Transactions on
, 2012
"... Dual energy computerized tomography has gained great interest because of its ability to characterize the chemical composition of a material rather than simply providing relative attenuation images as in conventional tomography. The purpose of this paper is to introduce a novel polychromatic dual ene ..."
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Dual energy computerized tomography has gained great interest because of its ability to characterize the chemical composition of a material rather than simply providing relative attenuation images as in conventional tomography. The purpose of this paper is to introduce a novel polychromatic dual energy processing algorithm with an emphasis on detection and characterization of piecewise constant objects embedded in an unknown, cluttered background. Physical properties of the objects, specifically the Compton scattering and photoelectric absorption coefficients, are assumed to be known with some level of uncertainty. Our approach is based on a levelset representation of the characteristic function of the object and encompasses a number of regularization techniques for addressing both the prior information we have concerning the physical properties of the object as well as fundamental, physicsbased limitations associated with our ability to jointly recover the Compton scattering and photoelectric absorption properties of the scene. In the absence of an object with appropriate physical properties, our approach returns a null characteristic function and thus can be viewed as simultaneously solving the detection and characterization problems. Unlike the vast majority of methods which define the level set function nonparametrically, i.e., as a dense set of pixel values), we define our level set parametrically via radial basis functions (RBF’s) and employ a GaussNewton type algorithm for cost minimization. Numerical results show that the algorithm successfully detects objects of interest, finds their shape and location, and gives a adequate reconstruction of the background. Index Terms Computed tomography, dualenergy, polychromatic spectrum, parametric level set, inverse problems, iterative reconstruction I.
GPUBASED VOLUME RECONSTRUCTION FROM VERY FEW ARBITRARILY ALIGNED XRAY IMAGES∗
"... Abstract. This paper presents a threedimensional GPUaccelerated algebraic reconstruction method in a fewprojection conebeam setting with arbitrary acquisition geometry. To achieve artifactreduced reconstructions in the challenging case of unconstrained geometry and extremely limited input data, ..."
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Abstract. This paper presents a threedimensional GPUaccelerated algebraic reconstruction method in a fewprojection conebeam setting with arbitrary acquisition geometry. To achieve artifactreduced reconstructions in the challenging case of unconstrained geometry and extremely limited input data, we use linear methods and an artifactavoiding projection algorithm to provide high reconstruction quality. We apply the conjugate gradient method in the linear case of Tikhonov regularization and the twopointstepsize gradient method in the nonlinear case of total variation regularization to solve the system of equations. By taking advantage of modern graphics hardware we achieve acceleration of up to two orders of magnitude over classical CPU implementations.