Search results for "Reconstruction algorithm"

showing 4 items of 34 documents

Spectral approach to D-bar problems

2017

We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2017 Wiley Periodicals, Inc.

[ MATH ] Mathematics [math]Spectral approachInverse conductivity problemBar (music)General MathematicsElectrical-impedance tomographyFOS: Physical sciences2 dimensions010103 numerical & computational mathematics01 natural sciencesDiscrete systemsymbols.namesakeConvergence (routing)FOS: MathematicsApplied mathematicsUniquenessStewartson-ii equationsMathematics - Numerical Analysis0101 mathematics[MATH]Mathematics [math]Electrical impedance tomographyReconstruction algorithmsNumerical-solutionMathematicsNonlinear Sciences - Exactly Solvable and Integrable SystemsApplied MathematicsNumerical Analysis (math.NA)Integral equation010101 applied mathematicsFourier transformsymbolsUniquenessExactly Solvable and Integrable Systems (nlin.SI)
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Phantomuntersuchung zur Optimierung der Spiral-CT und 3 D-Rekonstruktion des Tracheobronchialsystems

1996

PURPOSE To optimise three-dimensional spiral CT of the tracheobronchial tree using adequate acquisition and reconstruction parameters for spiral CT of the chest. MATERIAL AND METHODS Qualitative and quantitative assessment of different 3 D reconstructions of two test objects of the tracheobronchial tree depending on section thickness, reconstruction interval, pitch, and reconstruction algorithm used in spiral CT (Siemens, Somatom plus S) of the chest. The frequency of volume and stairstep artifacts was evaluated. The 3 D reconstructions were generated using a seeded VOI-technique (Allegro, ISG). RESULTS Reduction of artifacts was achieved by decreasing section thickness. Increasing overlap …

business.industryImage qualityQuantitative assessmentPitch factorRadiology Nuclear Medicine and imagingReconstruction algorithmImage processingIterative reconstructionNuclear medicinebusinessSpiral ctGeologySpiralRöFo - Fortschritte auf dem Gebiet der Röntgenstrahlen und der bildgebenden Verfahren
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High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

2011

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by expl…

lcsh:Medical physics. Medical radiology. Nuclear medicinelcsh:Medical technologyArticle SubjectComputer scienceStatistical noiseIterative methodImage qualitylcsh:R895-920ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONBasis functionReconstruction algorithmSpherical basisIterative reconstructioncomputer.software_genrelcsh:R855-855.5Radiology Nuclear Medicine and imagingData miningcomputerAlgorithmImage resolutionResearch ArticleComputingMethodologies_COMPUTERGRAPHICSInternational Journal of Biomedical Imaging
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Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities

2022

We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schr\"{o}dinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearit…

osittaisdifferentiaaliyhtälötincreasing stabilityreconstruction algorithmsApplied Mathematicspower type nonlinearitiesinversio-ongelmatComputer Science ApplicationsTheoretical Computer ScienceMathematics - Analysis of PDEsSignal ProcessingFOS: Mathematicsinverse Schrödinger potential problemMathematical PhysicsAnalysis of PDEs (math.AP)
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