Uncertainty quantification of CT regularized reconstruction within the Bayesian framework
Computed Tomography (CT) reconstruction is an important inverse problem in industrial imaging, requiring robust methods to address different sources of error in the data and model. Among the various reconstruction approaches that tackle different challenges in CT modeling [1], such as limitations i...
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2025-02-01
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| Series: | e-Journal of Nondestructive Testing |
| Online Access: | https://www.ndt.net/search/docs.php3?id=30731 |
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| author | Negin Khoeiniha Patricio Guerrero Wim Dewulf |
| author_facet | Negin Khoeiniha Patricio Guerrero Wim Dewulf |
| author_sort | Negin Khoeiniha |
| collection | DOAJ |
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Computed Tomography (CT) reconstruction is an important inverse problem in industrial imaging, requiring robust methods to address different sources of error in the data and model. Among the various reconstruction approaches that tackle different challenges in CT modeling [1], such as limitations in the data, statistical methods are known for their ability to model various properties [2, 3] of the input data and assess their impact on the reconstruction outcome [4]. These methods can also incorporate regularization techniques, which, for instance, force smoothness in the solution by penalizing heavy oscillations in pixel values. Given our interest in the uncertainty Quantification (UQ) of CT reconstruction, we employ statistical methods within the Bayesian framework for solving this inverse problem. First, we define a model for CT reconstruction and formulate a statistical framework for the problem. We then reconstruct our data using appropriate methods and quantify the uncertainty in the results. Our primary focus is on the effect of noise on the reconstruction and the corresponding uncertainty it induces. Additionally, we aim to utilize computationally feasible sampling techniques to analyze the distribution of the solution, enabling an in-depth evaluation of the results. To achieve these goals, we apply a rapid regularized Markov Chain Monte Carlo (MCMC) reconstruction method [4, 5], employing the Metropolis-Adjusted Langevin Algorithm (MALA) [6] and its Lipschitz-adaptive variant (LipMALA) [7]. This approach produces a volumetric model where each voxel is represented by a probability distribution, which can be transformed into a triplet of gray-value models: one for the central value and two for the bounds of the confidence interval. Bi-directional and uni-directional length measurements derived from these gray-value models applied to real CT data yield task-specific measurement uncertainties. This method significantly reduces computational and storage demands compared to classic Monte Carlo simulations while incorporating regularization techniques. Experimental results using aluminum cylindrical step gauge [8] data acquired with a Nikon 225 CT system validate our approach. This work provides a scalable, statistically grounded methodology for UQ in CT reconstruction, offering enhanced reliability for industrial applications.
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| format | Article |
| id | doaj-art-57ee36d5dd9544a783dbb78d24b275a7 |
| institution | Kabale University |
| issn | 1435-4934 |
| language | deu |
| publishDate | 2025-02-01 |
| publisher | NDT.net |
| record_format | Article |
| series | e-Journal of Nondestructive Testing |
| spelling | doaj-art-57ee36d5dd9544a783dbb78d24b275a72025-02-06T10:48:19ZdeuNDT.nete-Journal of Nondestructive Testing1435-49342025-02-0130210.58286/30731Uncertainty quantification of CT regularized reconstruction within the Bayesian frameworkNegin KhoeinihaPatricio GuerreroWim Dewulf Computed Tomography (CT) reconstruction is an important inverse problem in industrial imaging, requiring robust methods to address different sources of error in the data and model. Among the various reconstruction approaches that tackle different challenges in CT modeling [1], such as limitations in the data, statistical methods are known for their ability to model various properties [2, 3] of the input data and assess their impact on the reconstruction outcome [4]. These methods can also incorporate regularization techniques, which, for instance, force smoothness in the solution by penalizing heavy oscillations in pixel values. Given our interest in the uncertainty Quantification (UQ) of CT reconstruction, we employ statistical methods within the Bayesian framework for solving this inverse problem. First, we define a model for CT reconstruction and formulate a statistical framework for the problem. We then reconstruct our data using appropriate methods and quantify the uncertainty in the results. Our primary focus is on the effect of noise on the reconstruction and the corresponding uncertainty it induces. Additionally, we aim to utilize computationally feasible sampling techniques to analyze the distribution of the solution, enabling an in-depth evaluation of the results. To achieve these goals, we apply a rapid regularized Markov Chain Monte Carlo (MCMC) reconstruction method [4, 5], employing the Metropolis-Adjusted Langevin Algorithm (MALA) [6] and its Lipschitz-adaptive variant (LipMALA) [7]. This approach produces a volumetric model where each voxel is represented by a probability distribution, which can be transformed into a triplet of gray-value models: one for the central value and two for the bounds of the confidence interval. Bi-directional and uni-directional length measurements derived from these gray-value models applied to real CT data yield task-specific measurement uncertainties. This method significantly reduces computational and storage demands compared to classic Monte Carlo simulations while incorporating regularization techniques. Experimental results using aluminum cylindrical step gauge [8] data acquired with a Nikon 225 CT system validate our approach. This work provides a scalable, statistically grounded methodology for UQ in CT reconstruction, offering enhanced reliability for industrial applications. https://www.ndt.net/search/docs.php3?id=30731 |
| spellingShingle | Negin Khoeiniha Patricio Guerrero Wim Dewulf Uncertainty quantification of CT regularized reconstruction within the Bayesian framework e-Journal of Nondestructive Testing |
| title | Uncertainty quantification of CT regularized reconstruction within the Bayesian framework |
| title_full | Uncertainty quantification of CT regularized reconstruction within the Bayesian framework |
| title_fullStr | Uncertainty quantification of CT regularized reconstruction within the Bayesian framework |
| title_full_unstemmed | Uncertainty quantification of CT regularized reconstruction within the Bayesian framework |
| title_short | Uncertainty quantification of CT regularized reconstruction within the Bayesian framework |
| title_sort | uncertainty quantification of ct regularized reconstruction within the bayesian framework |
| url | https://www.ndt.net/search/docs.php3?id=30731 |
| work_keys_str_mv | AT neginkhoeiniha uncertaintyquantificationofctregularizedreconstructionwithinthebayesianframework AT patricioguerrero uncertaintyquantificationofctregularizedreconstructionwithinthebayesianframework AT wimdewulf uncertaintyquantificationofctregularizedreconstructionwithinthebayesianframework |