Tomographic X-ray data of a walnut

Hämäläinen, K.; Harhanen, Lauri; Kallonen, Aki; Kujanpää, Antti; Niemi, Esa; Siltanen, Samuli

doi:10.48550/arxiv.1502.04064

Cited by 15 publications

(23 citation statements)

References 2 publications

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“…We use two different test images from IR tools: the first one is called 'Three Phases', which has three regions, and the other is called 'Grains'. The second application comes from X-ray tomography and uses an open-source tomographic dataset corresponding to a walnut image [18]. A brief summary of the problem sizes and the number of level set functions used are summarized below: Level set parameters In the experiments, we choose the scale parameter = 10 −2 .…”

Section: Description Of the Test Problems And Parametersmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian Level Set Approach for Inverse Problems with Piecewise Constant Reconstructions

Reese¹,

Saibaba²,

Lee³

2021

Preprint

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There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the level set functions that determine the piecewise constant regions as well as the parameters that determine their magnitudes. We develop a Gauss-Newton approach with a backtracking line search to efficiently compute the maximum a priori (MAP) estimate as a solution to the inverse problem. We use the Gauss-Newton Laplace approximation to construct a Gaussian approximation of the posterior distribution and use preconditioned Krylov subspace methods to sample from the resulting approximation. To visualize the uncertainty associated with the parameter reconstructions we compute the approximate posterior variance using a matrix-free Monte Carlo diagonal estimator, which we develop in this paper. We will demonstrate the benefits of our approach and solvers on synthetic test problems (photoacoustic and hydraulic tomography, respectively a linear and nonlinear inverse problem) as well as an application to X-ray imaging with real data.

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Section: Description Of the Test Problems And Parametersmentioning

confidence: 99%

“…In this set of numerical experiments, we use the real-data from [18]. The dataset consists of the logarithm of the x-ray sinogram of a single two-dimensional slice of a walnut and the forward operator A modeling the x-ray transform for this particular set.…”

Section: X-ray Tomographymentioning

confidence: 99%

Bayesian Level Set Approach for Inverse Problems with Piecewise Constant Reconstructions

Reese¹,

Saibaba²,

Lee³

2021

Preprint

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show abstract

“…The final numerical result we present in Figure 8 is obtained using an image of a walnut reconstructed from CT data by the Finnish Inverse Problems Society [18] as the attenuation map. The walnut phantom for a is binary and so A = {0, 1}.…”

Section: Numerical Reconstructionsmentioning

confidence: 99%

Emission tomography with a multi-bang assumption on attenuation

Holman,

Richardson

2020

Preprint

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We consider the problem of joint reconstruction of both attenuation a and source density f in emission tomography in two dimensions. This is sometimes called the Single Photon Emission Computed Tomography (SPECT) identification problem, or referred to as attenuation correction in SPECT. Assuming that a takes only finitely many values and f ∈ C 1 c (R 2 ) we are able to characterise singularities appearing in the Attenuated Radon Transform Raf , which models emission tomography data. Using this characterisation we prove that both a and f can be determined in some circumstances. We also propose a numerical algorithm to jointly compute a and f from Raf based on a weakly convex regularizer when a only takes values from a known finite list, and show that this algorithm performs well on some synthetic examples.

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“…In order to demonstrate the practicality of our method, we computed results from nonsynthetic X-ray tomography data [8,28], which are available online. 2,3 See Figure 7 for these two examples ('lotus' and 'walnut').…”

Section: Numerical Examplesmentioning

confidence: 99%

Template-Based Image Reconstruction from Sparse Tomographic Data

et al. 2019

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We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass-or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for massand intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially.

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Tomographic X-ray data of a walnut

Cited by 15 publications

References 2 publications

Bayesian Level Set Approach for Inverse Problems with Piecewise Constant Reconstructions

Bayesian Level Set Approach for Inverse Problems with Piecewise Constant Reconstructions

Emission tomography with a multi-bang assumption on attenuation

Template-Based Image Reconstruction from Sparse Tomographic Data

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