Lecture Notes, Introduction to Inverse Problems

《Lecture Notes, Introduction to Inverse Problems》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、LectureNotes,IntroductiontoInverseProblemsGuillaumeBal1April21,20041DepartmentofAppliedPhysicsandAppliedMathematics,ColumbiaUniversity,NewYorkNY,10027;gb2030@columbia.eduContents1InverseproblemsandFouriertransforms31.1MagneticResonanceImaging(MRI)....................31.2Onedimensionalinversescat

2、teringproblem................51.3Fouriertransformsandwell-posedness....................71.4Hilbertscaleandill-posedness........................92TheRadontransform122.1TransmissionTomography..........................122.2Radontransforms...............................132.3ThreedimensionalRadontran

3、sform.....................203Inversekinematicproblem223.1Sphericalsymmetry..............................223.2AbelintegralandAbeltransform......................253.3KinematicInverseSourceProblem.....................253.4KinematicvelocityInverseProblem.....................284AttenuatedRadonTransfo

4、rm314.1SinglePhotonEmissionComputedTomography..............314.2RiemannHilbertproblem..........................324.3InversionoftheAttenuatedRadonTransform...............334.4Step(i):The∂problem,anellipticequation................344.5Step(ii):jumpconditions..........................364.6Step(iii)

5、:reconstructionformulas......................384.7Sourceproblemwithscattering.......................405Diffractiontomography435.1Scatteringproblem..............................435.2Farfielddataandreconstruction......................455.3ComparisontoX-raytomography......................476CauchyPro

6、blem496.1Electrocardiacpotential...........................496.2HalfSpaceProblem..............................506.2.1Electrocardiacapplication......................506.2.2Analyticcontinuation.........................526.3Generaltwodimensionalcase........................5216.3.1Laplaceequationona

7、nannulus...................536.3.2Riemannmappingtheorem......................537Atmosphericgasconcentrationreconstructions557.1Radiationmodeling..............................557.2Reconstructionofgasconcentrations............