6533b834fe1ef96bd129cc55

RESEARCH PRODUCT

Optimal recovery of a radiating source with multiple frequencies along one line

Joonas IlmavirtaTeemu TyniPetteri PiiroinenTommi Brander

subject

attenuated Radon transformMultispectralRAYUniqueness theorem01 natural sciencesinversio-ongelmat44A10 (Primary) 65R32 44A60 46N40 65Z05 (Secondary)030218 nuclear medicine & medical imaging0302 clinical medicine111 MathematicsDiscrete Mathematics and CombinatoricstietokonetomografiaPharmacology (medical)INVERSIONnuclear medicineBeam hardeningPhysicsLaplace transformDetectorNumerical Analysis (math.NA)Inverse problemuniqueness theoremFunctional Analysis (math.FA)Mathematics - Functional AnalysisMultiplicative system theoremkuvantaminensovellettu matematiikkaModeling and SimulationSPECTLine (geometry)numeerinen analyysipositroniemissiotomografiaemission computed tomographyAttenuated Radon transformEmission computed tomographyControl and OptimizationLaplace transformmultispectralOpen setCollimated light03 medical and health sciencesnuclear medicine.multiplicative system theoremFOS: Mathematicsinverse source problemMathematics - Numerical Analysis0101 mathematicsAttenuation010102 general mathematicsInverse source problemRangingComputational physicsTENSOR TOMOGRAPHYPETbeam hardeningNuclear MedicineAnalysis

description

We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.

yearjournalcountryeditionlanguage
2020-01-01
10.3934/ipi.2020044http://arxiv.org/abs/1905.08028