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Diffusion reconstruction from very noisy tomographic data

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  • As a consequence of very noisy tomographic data the reconstructed images are contaminated by severely amplified noise. Typically two remedies are considered. Firstly, the data are smoothed, this is called pre-whitening in the engineering literature. The disadvantage here is that the individually treated data sets could become inconsistent. Secondly, the image, reconstructed from the original data sets, is treated by methods of image smoothing. As example diffusion filters are mentioned. In this paper we present a method where the reconstruction of the smoothed image is performed in one step; i.e., we develop special reconstruction kernels, which directly compute the image smoothed by a diffusion filter. Examples from synthetic data are presented.
    Mathematics Subject Classification: Primary: 65R32; Secondary: 45Q05.

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