Computed Tomography Reconstruction with Uncertain View Angles by Iteratively Updated Model Discrepancy

Riis, Nicolai A. B.; Dong, Yiqiu; Hansen, Per Christian

doi:10.1007/s10851-020-00972-7

Cited by 7 publications

(23 citation statements)

References 28 publications

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“…Joint estimation of uncertain view angles determining the geometry of the forward CT model and the attenuation coefficient function of a scanned object is discussed in [20,21]. In [22], data-driven estimation of unknown fan-beam geometry is done by employing a neural network that learns the unknown forward operator from training data consisting of sinogram-image pairs.…”

Section: Related Workmentioning

confidence: 99%

Geometry Parameter Estimation for Sparse X-ray Log Imaging

Senchukova

Suuronen

Heikkinen³

et al. 2022

Preprint

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We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the source-detector pair, which creates the issue of unknown geometry. This work considers two approaches for geometry estimation. Our first approach is a calibration object correlation method in which we calculate the maximum cross-correlation between a known-sized calibration object image and its filtered backprojection reconstruction and use differential evolution as an optimiser. The second approach is projection trajectory simulation, where we use a set of known intersection points and a sequential Monte Carlo method for estimating the posterior density of the parameters. We show numerically that a large set of parameters can be used for artefact-free reconstruction. We deploy Bayesian inversion with Cauchy priors for synthetic and real sawmill data for detection of knots with a very low number of measurements and uncertain measurement geometry.

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Section: Related Workmentioning

confidence: 99%

Geometry Parameter Estimation for Sparse X-ray Log Imaging

Senchukova

Suuronen

Heikkinen³

et al. 2022

Preprint

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“…Our paper is structured as follows. In Section 2 we summarize our previous work in [24], where we derive a CT reconstruction method that takes uncertainty in the view angles into account by marginalization. In Section 3 we propose our new method which additionally estimates the view angles and the associated uncertainty by jointly estimating the view angles and the CT image in an iterative procedure.…”

Section: Structure Of Papermentioning

confidence: 99%

“…If it is not valid, we lose the block structure of L ν|x and then we need to replace SPDHG by other solvers in order to handle the large and dense matrix L ν|x . We refer to our previous work in [24] for more details on efficient computation of the solution to (10).…”

Section: Ct Image Reconstructionmentioning

confidence: 99%

“…Similarly, as we show in [24], the data-fitting term in (10) can be split into q data-fitting terms arriving as the image reconstruction model…”

Section: Block Representation Of Covariance Matricesmentioning

confidence: 99%

“…The optimization problem with respect to the reconstruction x in line 13 is solved by using a stochastic primal-dual hybrid gradient algorithm [8]. For more details on solving the CT problem see [24]. Note that line 13 can be replaced by other effective reconstruction methods.…”

Section: Alternating Scheme For Image Reconstruction and View Angle E...mentioning

confidence: 99%

See 2 more Smart Citations

Computed tomography with view angle estimation using uncertainty quantification

Riis¹,

Dong²,

Hansen³

2021

Inverse Problems

Self Cite

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We consider computed tomography (CT) with uncertain measurement geometry, with a focus on the case where the view angles are uncertain and where estimation of these angles improves the reconstruction. We propose a new reconstruction model and a corresponding algorithm that has an additional view-angle estimation component, allowing us to determine the angles solely from the measured CT data. A key component of our approach is that we quantify the uncertainty of the view angles via a model-discrepancy formulation, allowing us to take the uncertainty into account in the image reconstruction. This approach generalizes in a straightforward way to other cases of uncertain geometry. Our method is computationally efficient since we can utilize a block-structure of the computational problem for estimation of both the CT image and the view angles under the assumption that the view angles are independent. The joint image/angle reconstruction problem is non-convex which leads to difficulties in recently proposed algorithms, and we demonstrate numerically that our method seems to avoid these difficulties. Simulations show that our method, with a total variation prior that reflects our phantoms, is able to achieve reconstructions whose quality is similar to ones obtained with the correct view angles (the ideal scenario).

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Geometry Parameter Estimation for Sparse X-Ray Log Imaging

Senchukova,

Suuronen,

Heikkinen

et al. 2023

J Math Imaging Vis

View full text Add to dashboard Cite

We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the source–detector pair, which creates the issue of unknown geometry. This work considers an approach for geometry estimation based on the calibration object. We parametrise the geometry using a set of 5 parameters. To estimate the geometry parameters, we calculate the maximum cross-correlation between a known-sized calibration object image and its filtered backprojection reconstruction and use differential evolution as an optimiser. The approach allows estimating geometry parameters from full-angle measurements as well as from sparse measurements. We show numerically that different sets of parameters can be used for artefact-free reconstruction. We deploy Bayesian inversion with first-order isotropic Cauchy difference priors for reconstruction of synthetic and real sawmill data with a very low number of measurements.

show abstract

Computed Tomography Reconstruction with Uncertain View Angles by Iteratively Updated Model Discrepancy

Cited by 7 publications

References 28 publications

Geometry Parameter Estimation for Sparse X-ray Log Imaging

Geometry Parameter Estimation for Sparse X-ray Log Imaging

Computed tomography with view angle estimation using uncertainty quantification

Geometry Parameter Estimation for Sparse X-Ray Log Imaging

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