Search results for "Inverse source problem"

showing 2 items of 2 documents

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

2020

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.

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
researchProduct

Radiating and non-radiating sources in elasticity

2018

In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.

Enclosure010103 numerical & computational mathematicsNavier equation01 natural sciencesinversio-ongelmatTheoretical Computer ScienceMathematics - Analysis of PDEsFOS: Mathematics0101 mathematicsMathematical PhysicsPhysicselastic wavesApplied MathematicsMathematical analysisRegular polygonElasticity (physics)EigenfunctionComputer Science ApplicationsExponential function010101 applied mathematicsInverse source probleminverse source problemsSignal Processingexponential solutions transmission eigenfunctionsFixed frequencyAnalysis of PDEs (math.AP)
researchProduct