Pré-Publication, Document De Travail Année : 2016

An iterative inversion of weighted Radon transforms along hyperplanes

Résumé

We propose iterative inversion algorithms for weighted Radon transforms RW along hyperplanes in R3. More precisely, expanding the weight W=W(x,θ),xR3,θS2 , into the series of spherical harmonics in θ and assuming that the zero order term w0,0(x) is not zero at any xR3 , we reduce the inversion of RW to solving a linear integral equation. In addition, under the assumption that the even part of W in θ (i.e., 1/2(W(x,θ)+W(x,θ))) is close to w0,0, the aforementioned linear integral equation can be solved by the method of successive approximations. Approximate inversions of RW are also given. Our results can be considered as an extension to 3D of two-dimensional results of Kunyansky (1992), Novikov (2014), Guillement, Novikov (2014). In our studies we are motivated, in particular, by problems of emission tomographies in 3D. In addition, we generalize our results to the case of dimension n>3.
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Dates et versions

hal-01405387 , version 1 (29-11-2016)
hal-01405387 , version 2 (09-06-2017)
hal-01405387 , version 3 (05-07-2017)
hal-01405387 , version 4 (14-09-2017)

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Citer

F O Goncharov. An iterative inversion of weighted Radon transforms along hyperplanes. 2016. ⟨hal-01405387v3⟩
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