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Попов, Д. А.

doi:10.1023/a:1013126507543

Cited by 7 publications

(2 citation statements)

References 20 publications

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“…Alternative results are in [Bey84,Pop01] (see also [Pop03]). It is shown in [Bey84] that by selecting the appropriate dual RT R * and singular convolution operator K, one has E := R * KR − Id is a PDO of order −1, and the norm of E : L 2 0 (U ) → L 2 loc (U ) goes to zero if → 0.…”

Section: Introductionmentioning

confidence: 99%

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An accurate approximate algorithm for motion compensation in two-dimensional tomography

Katsevich

2010

Inverse Problems

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In this paper, we propose two approximate inversion formulae for motion compensation in tomography: for parallel beam and fan beam geometries. Let E denote the operator, which corresponds to the error term of an inversion formula. It is proven that in both cases E : H m 0 → H m+1 0 is bounded; thus, the error term is one order smoother than the original function f in the scale of Sobolev spaces. It is also proven that in both cases if the motion map approaches the identity map, then the norm of E approaches zero. The formulae can be easily implemented numerically. Results of numerical experiments in the fanbeam case (which is more common in applications) demonstrate good image quality even when motion is relatively strong.

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Section: Introductionmentioning

confidence: 99%

“…Assuming that the manifold of curves is sufficiently close to the family of straight lines (i.e. when → 0), the following results are established in [Pop01]:…”

Section: Introductionmentioning

confidence: 99%