Reflective tomography recovers the surfaces of a scene to be imaged, from optical images: a tomographic algorithm computes a full volumic reconstruction and then the surfaces are extracted from this reconstruction. For better performance, we would like to avoid computing accurately the full reconstruction, and we want to focus computations on the sought surfaces. For that purpose we propose an iterative multiresolution process. The initialization computes a coarse reconstruction, and the iterations refines it. To identify the voxels to be refined, we take advantage of the asymptotic behaviour of the reconstruction, with respect to its cut-off frequency: it discriminates the surfaces to be extracted. By the way the proposed algorithm is greedy: each iteration maximizes the accumulated intensity of the selected voxels, with prescribed volume. The combination of the complexity analysis and the numerical results shows that this novel approach succeeds in reconstructing surfaces and is relatively efficient compared with the standard method. These works pave the way towards accelerated algorithms in reflective tomography. They can be extended to a general class of problems concerning the determination of asymptotically discriminated sets, what is related to the computation of singular support of distributions.
DOI: 10.5802/smai-jcm.35
Keywords: Computational optics, reconstruction, acceleration, complexity
CC-BY-NC-ND 4.0
@article{SMAI-JCM_2018__4__259_0,
author = {Jean-Baptiste Bellet},
title = {Multiresolution greedy algorithm dedicated to reflective tomography},
journal = {The SMAI Journal of computational mathematics},
pages = {259--296},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {4},
year = {2018},
doi = {10.5802/smai-jcm.35},
zbl = {1416.78009},
mrnumber = {3867963},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.35/}
}
TY - JOUR AU - Jean-Baptiste Bellet TI - Multiresolution greedy algorithm dedicated to reflective tomography JO - The SMAI Journal of computational mathematics PY - 2018 SP - 259 EP - 296 VL - 4 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.35/ DO - 10.5802/smai-jcm.35 LA - en ID - SMAI-JCM_2018__4__259_0 ER -
%0 Journal Article %A Jean-Baptiste Bellet %T Multiresolution greedy algorithm dedicated to reflective tomography %J The SMAI Journal of computational mathematics %D 2018 %P 259-296 %V 4 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.35/ %R 10.5802/smai-jcm.35 %G en %F SMAI-JCM_2018__4__259_0
Jean-Baptiste Bellet. Multiresolution greedy algorithm dedicated to reflective tomography. The SMAI Journal of computational mathematics, Volume 4 (2018), pp. 259-296. doi : 10.5802/smai-jcm.35. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.35/
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