Multiresolution greedy algorithm dedicated to reflective tomography

Bellet, Jean-Baptiste

The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 259-296.

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.

Classification : 78A97, 94A12, 65B99, 65Y20
Mots clés : Computational optics, reconstruction, acceleration, complexity

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