Easy implementation of advanced tomography algorithms using the ASTRA toolbox with Spot operators

Bleichrodt, Folkert; Leeuwen, Tristan van; Palenstijn, Willem Jan; Aarle, Wim van; Sijbers, Jan; Batenburg, Kees Joost

doi:10.1007/s11075-015-0016-4

Cited by 27 publications

(20 citation statements)

References 36 publications

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“…This can lead to an error in the gradient computation. However, these errors are typically much smaller than the desired tolerances, so we do not see their effect in practice [37]. The presented results can be reproduced using open-source codes [38].…”

Section: Numerical Experimentsmentioning

confidence: 97%

A Novel Tomographic Reconstruction Method Based on the Robust Student's t Function For Suppressing Data Outliers

Kazantsev

Bleichrodt

Leeuwen

et al. 2017

IEEE Trans. Comput. Imaging

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Regularized iterative reconstruction methods in computed tomography can be effective when reconstructing from mildly inaccurate undersampled measurements. These approaches will fail, however, when more prominent data errors, or outliers, are present. These outliers are associated with various inaccuracies of the acquisition process: defective pixels or miscalibrated camera sensors, scattering, missing angles, etc. To account for such large outliers, robust data misfit functions, such as the generalized Huber function, have been applied successfully in the past. In conjunction with regularization techniques, these methods can overcome problems with both limited data and outliers. This paper proposes a novel reconstruction approach using a robust data fitting term which is based on the Student’s t distribution. This misfit promises to be even more robust than the Huber misfit as it assigns a smaller penalty to large outliers. We include the total variation regularization term and automatic estimation of a scaling parameter that appears in the Student’s t function. We demonstrate the effectiveness of the technique by using a realistic synthetic phantom and also apply it to a real neutron dataset

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Section: Numerical Experimentsmentioning

confidence: 97%

A Novel Tomographic Reconstruction Method Based on the Robust Student's t Function For Suppressing Data Outliers

Kazantsev

Bleichrodt

Leeuwen

et al. 2017

IEEE Trans. Comput. Imaging

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“…For FDK reconstructions, the experiments were performed on Intel(R) Xeon(R) CPU E5-1650 v3 at 3.7GHz RAM 32 and GPU 4GB memory. The ASTRA Toolbox (iMinds-Vision Lab, University of Antwerp, Belgium) and Spot operator were used in reconstructions [30], [36], [37]. The CSDS computations was performed on CPU at supercluster taito.csc.fi.…”

Section: B Morphometrics Parameters Values Using Different Sparsity mentioning

confidence: 99%

An Automatic Regularization Method: An Application for 3-D X-Ray Micro-CT Reconstruction Using Sparse Data

Purisha

Karhula

Ketola

et al. 2019

IEEE Trans. Med. Imaging

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X-ray tomography is a reliable tool for determining the inner structure of 3D object with penetrating X-rays. However, traditional reconstruction methods such as FDK require dense angular sampling in the data acquisition phase leading to long measurement times, especially in X-ray micro-tomography to obtain high resolution scans. Acquiring less data using greater angular steps is an obvious way for speeding up the process and avoiding the need to save huge data sets. However, computing 3D reconstruction from such a sparsely sampled dataset is difficult because the measurement data is usually contaminated by errors and linear measurement models do not contain sufficient information to solve the problem in practice. An automatic regularization method is proposed for robust reconstruction, based on enforcing sparsity in the three-dimensional shearlet transform domain. The inputs of the algorithm are the projection data and a priori known expected degree of sparsity, denoted 0 < Cpr ≤ 1. The number Cpr can be calibrated from a few dense-angle reconstructions and fixed. Human subchondral bone samples were tested and morphometric parameters of the bone reconstructions were then analyzed using standard metrics. The proposed method is shown to outperform the baseline algorithm (FDK) in the case of sparsely collected data. The number of X-ray projections can be reduced up to 10% of the total amount 300 projections over 180 degrees with uniform angular step while retaining the quality of the reconstruction images and of the morphometric parameters.

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“…where the expressions for the gradient and Gauss-Newton Hessian are given by (4). Convergence of this alternating approach to a local minimum of (7) is guaranteed as long as the step-length satisfies the strong Wolfe conditions [16].…”

Section: Joint Reconstruction Algorithmmentioning

confidence: 99%

“…We also add Gaussian noise of 10 dB SNR to this synthetic data. To check the performance of the proposed method, we compare it to Total-variation method [4], DART [3] and its modified version for partially discrete tomography, P-DART [13]. A total of 200 iterations were performed with regularization parameter determined from shape residual curve.…”

Section: Limited-angle Testmentioning

confidence: 99%

A Parametric Level-Set Method for Partially Discrete Tomography

Kadu

Leeuwen

Batenburg

2017

Discrete Geometry for Computer Imagery

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This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We represent the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimization problem in terms of the background and coefficients for the level-set function. To constrain the background reconstruction we impose smoothness through Tikhonov regularization. The bi-level optimization problem is solved in an alternating fashion; in each iteration we first reconstruct the background and consequently update the level-set function. We test our method on numerical phantoms and show that we can successfully reconstruct the geometry of the anomaly, even from limited data. On these phantoms, our method outperforms Total Variation reconstruction, DART and P-DART.

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Easy implementation of advanced tomography algorithms using the ASTRA toolbox with Spot operators

Cited by 27 publications

References 36 publications

A Novel Tomographic Reconstruction Method Based on the Robust Student's t Function For Suppressing Data Outliers

A Novel Tomographic Reconstruction Method Based on the Robust Student's t Function For Suppressing Data Outliers

An Automatic Regularization Method: An Application for 3-D X-Ray Micro-CT Reconstruction Using Sparse Data

A Parametric Level-Set Method for Partially Discrete Tomography

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