Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery principles

Cerejeiras, Paula; Ferreira, Milton; Kaehler, Uwe; Teschke, Gerd

http://hdl.handle.net/10400.8/3815

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Abstract(s)

The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill-posed inverse problem that can be applied to X-ray tomography with polycrystalline materials. This paper is concerned with the development of a method to stably approximate the inverse of the noisy Radon transform on SO(3). The proposed approach is composed by basic building blocks of the coorbit theory on homogeneous spaces, Gabor frame constructions and variational principles for sparse recovery. The performance of the finally obtained iterative approximation is studied through several experiments.

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Acknowledgements: The research of P. Cerejeiras, M. Ferreira, and U. Kähler was (partially) supported by Unidade de Investigação Matemática e Aplicações of Universidade de Aveiro, through Programa Operacional Ciência, Tecnologia, Inovação (POCTI) of the Fundação para a Ciência e a Tecnologia (FCT), co nanced by the European Community fund FEDER. G. Teschke gratefully acknowledges support by DAAD Grant D/07/13641

Keywords

Radon transform on SO(3) X-ray tomography Gabor frames Coorbit theory Sparse recovery Crystallography

URI

http://hdl.handle.net/10400.8/3815

Citation

Cerejeiras P., Ferreira M., Kähler U., and Teschke G., Inversion of the noisy Radon transform on SO(3) by Gabor frames and sparse recovery algorithms, Appl. Comput. Harmon. Anal., 31 (3) (2011), 325-345