6533b7defe1ef96bd127688b

RESEARCH PRODUCT

Fourier analysis of periodic Radon transforms

Jesse Railo

subject

Pure mathematicsGeneral MathematicsBessel potential01 natural sciencesTikhonov regularizationsymbols.namesakeFOS: Mathematics0101 mathematicsperiodic distributionsMathematicsRadon transformRadon transformApplied Mathematics44A12 42B05 46F12 45Q05010102 general mathematicsZero (complex analysis)Function (mathematics)Fourier analysisFunctional Analysis (math.FA)010101 applied mathematicsSobolev spaceregularizationMathematics - Functional AnalysisDistribution (mathematics)Fourier analysissymbolsAnalysis

description

We study reconstruction of an unknown function from its $d$-plane Radon transform on the flat $n$-torus when $1 \leq d \leq n-1$. We prove new reconstruction formulas and stability results with respect to weighted Bessel potential norms. We solve the associated Tikhonov minimization problem on $H^s$ Sobolev spaces using the properties of the adjoint and normal operators. One of the inversion formulas implies that a compactly supported distribution on the plane with zero average is a weighted sum of its X-ray data.

yearjournalcountryeditionlanguage
2019-09-01
10.1007/s00041-020-09775-1http://arxiv.org/abs/1909.00495