Bayesian inversion method for 3D dental X-ray imaging

Kolehmainen, Ville; Vanne, Antti; Siltanen, Samuli; Järvenpää, Seppo; Kaipio, Jari P.; Lassas, Matti; Kalke, Martti

doi:10.1007/s00502-007-0450-7

Cited by 8 publications

(7 citation statements)

References 29 publications

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“…This variant of the projected gradient method involves a Barzilai-Borwein steplength (Barzilai and Borwein, 1988) and a linesearch to ensure convergence. Due to its simplicity and efficiency, SPG is used for inverse problems in engineering applications (Birgin, Martínez, and Raydan, 2014, section 4), including image deblurring (Bonettini, Zanella, and Zanni, 2008) and radiology (Kolehmainen, Vanne, Siltanen, Jarvenpaa, Kaipio, Lassas, and Kalke, 2006;Kolehmainen, Vanne, Siltanen, Järvenpää, Kaipio, Lassas, and Kalke, 2007).…”

Section: Motivation and Previous Workmentioning

confidence: 99%

Scaled projected-directions methods with application to transmission tomography

2020

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Statistical image reconstruction in X-Ray computed tomography yields large-scale regularized linear least-squares problems with nonnegativity bounds, where the memory footprint of the operator is a concern. Discretizing images in cylindrical coordinates results in significant memory savings, and allows parallel operator-vector products without on-the-fly computation of the operator, without necessarily decreasing image quality. However, it deteriorates the conditioning of the operator. We improve the Hessian conditioning by way of a blockcirculant scaling operator and we propose a strategy to handle nondiagonal scaling in the context of projected-directions methods for bound-constrained problems. We describe our implementation of the scaling strategy using two algorithms: TRON, a trust-region method with exact second derivatives, and L-BFGS-B, a linesearch method with a limited-memory quasi-Newton Hessian approximation. We compare our approach with one where a change of variable is made in the problem. On two reconstruction problems, our approach converges faster than the change of variable approach, and achieves much tighter accuracy in terms of optimality residual than a first-order method.

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Section: Motivation and Previous Workmentioning

confidence: 99%

Scaled projected-directions methods with application to transmission tomography

2020

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“…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].…”

Section: S 250mentioning

confidence: 99%

“…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].…”

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confidence: 99%

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

Groß¹,

Heil²,

Schulze³

et al. 2010

SIAM J. Sci. Comput.

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Abstract. This paper presents a three-dimensional GPU-accelerated algebraic reconstruction method in a few-projection cone-beam setting with arbitrary acquisition geometry. To achieve artifact-reduced reconstructions in the challenging case of unconstrained geometry and extremely limited input data, we use linear methods and an artifact-avoiding projection algorithm to provide high reconstruction quality. We apply the conjugate gradient method in the linear case of Tikhonov regularization and the two-point-step-size 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.

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“…In some medical applications, it is enough to consider slices of the reconstruction where the stable part of the wavefront set reliably provides the clinically important boundaries of tissues. For example, in [81] the spatial position of microcalcifications in the breast can be recovered, and the slice considered in [55] provides a low-dose x-ray examination for dental implant planning. However, any new method that is able to recover the missing part of the wavefront set more reliably would improve the quality of those reconstructions and lead to unprecedented applications of limited angle tomography.…”

Section: Introductionmentioning

confidence: 99%

Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography

et al. 2019

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The high complexity of various inverse problems poses a significant challenge to modelbased reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based methodologies such as deep learning. However, in the context of inverse problems, deep neural networks mostly act as black box routines, used for instance for a somewhat unspecified removal of artifacts in classical image reconstructions. In this paper, we will focus on the severely ill-posed inverse problem of limited angle computed tomography, in which entire boundary sections are not captured in the measurements. We will develop a hybrid reconstruction framework that fuses model-based sparse regularization with data-driven deep learning. Our method is reliable in the sense that we only learn the part that can provably not be handled by model-based methods, while applying the theoretically controllable sparse regularization technique to the remaining parts. Such a decomposition into visible and invisible segments is achieved by means of the shearlet transform that allows to resolve wavefront sets in the phase space. Furthermore, this split enables us to assign the clear task of inferring unknown shearlet coefficients to the neural network and thereby offering an interpretation of its performance in the context of limited angle computed tomography.Our numerical experiments show that our algorithm significantly surpasses both pure model-and more data-based reconstruction methods.

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Bayesian inversion method for 3D dental X-ray imaging

Cited by 8 publications

References 29 publications

Scaled projected-directions methods with application to transmission tomography

Scaled projected-directions methods with application to transmission tomography

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

Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography

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