Search results for "Radon transform."

showing 3 items of 23 documents

Needle-shape quality control by shadowgraphic image processing

2011

International audience; We propose a needle-shape quality-control method. To this end, we have devised a new acquisition system that combines a camera and a backlight. Needle measurements are carried out at a micrometric scale using shadowgraphic image processing. Our method not only distinguishes good needles from bad ones, but also allows classifying flawed needles into various categories of defects. This classification is important because some categories of defects can affect the entire production, whereas others do not. The results of our needle-shape quality-control method are validated using real samples directly off the manufacturing line. Needles are correctly classified at >97%, a…

[ INFO.INFO-TS ] Computer Science [cs]/Signal and Image ProcessingComputer scienceImage qualityImage processing[ SPI.SIGNAL ] Engineering Sciences [physics]/Signal and Image processing02 engineering and technologyBacklightMathematical morphology[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processingneedle020204 information systems[ INFO.INFO-TI ] Computer Science [cs]/Image Processing0202 electrical engineering electronic engineering information engineeringComputer visionquality controlImage sensorRadon transformbusiness.industryGeneral EngineeringImage segmentationAtomic and Molecular Physics and Opticsimage processingmetrology[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]020201 artificial intelligence & image processingArtificial intelligencebusiness[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processingShape analysis (digital geometry)Optical Engineering
researchProduct

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

Applications of Microlocal Analysis in Inverse Problems

2020

This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019.

radon transformRadon transforminverse problemsGeneral Mathematicslcsh:Mathematics010102 general mathematicscalderón problemMicrolocal analysisDirichlet-to-Neumann mapInverse problemlcsh:QA1-93901 natural sciencesinversio-ongelmatGel’fand problem010104 statistics & probabilitymicrolocal analysisComputer Science (miscellaneous)Calculus0101 mathematicsPostgraduate levelEngineering (miscellaneous)MathematicsMathematics
researchProduct