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Spherically symmetric volume elements as basis functions for image reconstructions in computed laminography

: Trampert, Patrick; Vogelgesang, Jonas; Schorr, Christian; Maisl, Michael; Bogachev, Sviatoslav; Marniok, Nico; Louis, Alfred; Dahmen, Tim; Slusallek, Philipp

Preprint (PDF; )

Journal of X-ray science and technology 25 (2017), Nr.4, S.533-546
ISSN: 0895-3996
ISSN: 1095-9114
Deutsche Forschungsgemeinschaft DFG
Deutsche Forschungsgemeinschaft DFG
MA 5836/1-1
Deutsche Forschungsgemeinschaft DFG
SL 38/5-1
Zeitschriftenaufsatz, Elektronische Publikation
Fraunhofer IZFP ()
computed laminography; blob basis function; simultaneous algebraic reconstruction technique; SART; Kaiser-Bessel window

BACKGROUND: Laminography is a tomographic technique that allows three-dimensional imaging of flat and elongated objects that stretch beyond the extent of a reconstruction volume. Laminography images can be reconstructed using iterative algorithms based on the Kaczmarz method.
OBJECTIVE: This study aims to develop and demonstrate a new reconstruction algorithm that may provide superior image reconstruction quality for this challenged imaging application.
METHODS: The images are initially represented using the coefficients over basis functions, which are typically piecewise constant functions (voxels). By replacing voxels with spherically symmetric volume elements (blobs) based on the generalized Kaiser-Bessel window functions, the images are reconstructed using this new adapted version of the algebraic image reconstruction technique.
RESULTS: Band-limiting properties of blob functions are beneficial particular in the case of noisy projections andwith only a limited number of available projections. Study showed that using blob basis functions improved full-width-at-half-maximum resolution from 10.2±1.0 to 9.9±0.9 (p < 0.001). Signal-to-noise ratio also improved from 16.1 to 31.0. The increased computational demand per iteration was compensated by using a faster convergence rate, such that the overall performance is approximately identical for blobs and voxels.
CONCLUSIONS: Despite the higher complexity, tomographic reconstruction from computed laminography data should be implemented using blob basis functions, especially if noisy data is expected.