Parallel Iterative Methods with A Priori Information for Robust Computed Laminography of Low Contrast, Difficult-To-Measure Objects
Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
Final Report Abstract
The goal of this project was to build a novel pipeline based on Computed Laminography (CL) to allow for a robust and reliable non-destructive testing of low-contrast, difficult-to-measureobjects, which involved mathematical algorithm development and highly-efficient parallel software implementations. Tomographic reconstructions for laminographic datasets can in principle be achieved using block iterative algorithms from the Kaczmarz or Landweber class of methods. However, contrary to single axis computed tomography, the problem cannot be solved sliced-by-slice but must be considered inherently in 3D dimensions. Interestingly, the same situation arises for a wider class of tomographic reconstruction problems with complex acquisition geometry, such as synchrotron X-Ray laminography, conical tilt electron tomography, and combined tilt- and focal series electron tomography. The software package Ettention was implemeted to address this class of problems, allowing for arbitrary projection geometries on large datasets and maintain high reconstruction performance. A mathematical framework was developed to handle and analyse systems of bounded linear operators as arising in CT and CL applications for non-standard acquisition geometries, allowing for a separate analysis and evaluation of the chosen basis functions and the used method for solving the reconstruction problem. The derived framework was applied to cone beam related geometries as the reconstruction problem for CLARA datasets and an iterative reconstruction method was proposed. It was found that the widely-used and well-known classical fomulation of SART is a special case of this method, and thus was used as a basis for the implementations. Geometrical as well as material prior information was successfully incorporated into the reconstruction, resulting in a more accurate model of the underlying scanning process. The alignment problem was successfully solved proposing two different algorithms. The registration problem of matching the geometrical a priori information with the measured data was solved successfully with the proposed 3D-3D and 2D-3D registration methods, whereas the second one is also applicable for the ROI problem. The ROI reconstruction problem for objects of almost homogeneous material was solved by applying a correction factor derived within the semi-discrete mathematical framework. The ROI reconstructions were evaluated using the ray-length corrected version of the SART derived for geometrical prior knowledge. The algorithms and the choice of basis functions, especially the use of the blob basis functions, were evaluated for laminography datasets, and varying setups, so that different levels of noise and different number of input projections for the reconstruction could be tested. These setups reflected a varying amount of radiation dose, whereby noisier datasets as well as fewer projections constituted less dose. To conclude, a pipeline for laminographic measurements based on the CLARA geometry was developed and implemented. All data processing issues such as alignment problems were solved successfully. We introduced a semi-discrete framework providing iterative methods to successsfully reconstruct laminographic data, with the classical SART method being a special case. In difficult to measure situations such as low signal-to-noise ratio or poor contrast, the choice of basis functions for the discretization and the incorporation of geometric prior knowledge can lead to enhanced reconstruction quality. The increased computational demand of these methods can be compensated by low-level optimization of the reconstruction software.
Publications
- (2017) Iterative Region-of-Interest Reconstruction from Limited Data Using Prior Information. Sens Imaging (Sensing and Imaging) 18 (1)
Vogelgesang, Jonas; Schorr, Christian
(See online at https://doi.org/10.1007/s11220-017-0165-8) - (2017) Spherically symmetric volume elements as basis functions for image reconstructions in computed laminography. Journal of X-ray science and technology 25 (4) 533-546
Trampert, Patrick; Vogelgesang, Jonas; Schorr, Christian; Maisl, Michael; Bogachev, Sviatoslav; Marniok, Nico; Louis, Alfred; Dahmen, Tim; Slusallek, Philipp
(See online at https://doi.org/10.3233/XST-16230) - Combined reconstruction and edge detection in dimensioning. Measurement Science and Technology 24, 125601. 2013
Hahn, B.N., Louis, A.K., Maisl, M. and Schorr, C.
(See online at https://doi.org/10.1088/0957-0233/24/12/125601) - Applying a priori Information to computed laminography. Proceedings of the Digital Industrial Radiology and Computed Tomography (DIR 2015). pp. 22-25
Dörr, L., Maisl, M. and Schorr, C.
- Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series. Microscopy and Microanalysis 21(03). 2015, pp. 725-738
Dahmen, T., Kohr, H., de Jonge, N. and Slusallek, P.
(See online at https://doi.org/10.1017/S1431927615000525) - A Semi-Discrete Landweber–Kaczmarz Method for Cone Beam Tomography and Laminography Exploiting Geometric Prior Information. Sensing and Imaging 17(17). 2016
Vogelgesang, J. and Schorr, C.
(See online at https://doi.org/10.1007/s11220-016-0142-7) - Advanced recording schemes for electron tomography. MRS Bulletin, 41(07). 2016, pp. 537–541
Dahmen, T., Trampert, P., de Jonge, N. and Slusallek, P.
(See online at https://doi.org/10.1557/mrs.2016.135) - Reconstruction of fluid flows in porous media using geometric a priori information. Review of Scientific Instruments. 2016
Maisl, M., Scholl, H., Schorr, C. and Seemann, R.
(See online at https://doi.org/10.1063/1.4971301) - The Ettention software package. Ultramicroscopy, 161. 2016, pp. 110-118
Dahmen, T., Marsalek, L., Marniok, N., Turoňová, B., Bogachev, S., Trampert, P., Nickels, S. and Slusallek, P.
(See online at https://doi.org/10.1016/j.ultramic.2015.10.012)
