Handbook of Mathematical Methods in Imaging

1619 Pages·2011·37.932 MB·English

by  Charles Groetsch (auth.), Otmar Scherzer (eds.)

HandbookofMathematicalMethodsinImaging

Otmar Scherzer(Ed.)
Handbook of
Mathematical Methods
in Imaging
withFiguresandTables
123
Editor:
OtmarScherzer
ComputationalScienceCenter
UniversityofVienna
Nordbergstrasse
Vienna
Austria
and
RICAM
AustrianAcademyofSciences
Linz
Austria
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Preface
Today,computerimagingcoversvariousaspectsofdatafiltering,patternrecognition, feature
extraction,computeraideddesign,andcomputeraidedinspectionanddiagnosis.
Pillarsofthefieldofcomputerimagingareadvanced,stable,andreliablealgorithms.In
addition,feasibilityanalysisisrequiredtoevaluatepracticalrelevanceofthemethods.To
putthesepillarsonsolidgrounds,asignificantamountofmathematicaltoolsarerequired.
Thishandbookmakesahumbleattempttoprovideasurveyofsuchmathematicaltools.
We had the vision that this imaging handbook should contain individual chapters
whichcanserveastoolboxes,which,whenaligned,formbackgroundmaterialforcomplete
appliedimagingproblems.Thereforeitshouldalsogiveanimpressiononthebroadmathe-
matical knowledge required to solve industrial and applied research applications: The
imageformationprocess,veryfrequently,isassignedtotheinverseproblemscommunity,
whichisprominentlyrepresentedinthishandbook.Thesubsequentstepisimageanalysis.
Nowadays,advancedImageAnalysis,andImageProcessingingeneral,usessophisticated
methodsfromGeometry,DifferentialGeometry,ConvexAnalysis,NumericalAnalysis,to
mentionjustafew.Infact,bytherapidadvanceofImaging,themathematical areashave
beenpushedforwardheavily,andraisedtheirimpactinapplicationsciences.
Myspecialthanksgotoallindividualauthorsfortheirvaluablecontributionsandthe
refereesfortheirhelpinimprovingthecontributionsandmakingdetailedcomments.My
sincerethanksgototheSpringer’seditorsandstaff,VaishaliDamle,JenniferCarlson,and
SaskiaEllisfortheirpatience,andtheirconstantsupportandencouragementoverthelast
twoyears.
Finally,Iwouldliketoencouragethereaderstosubmitsuggestionsregardingthehand-
book’s content. For a projectof this size, itislikely that essential topicsare missed. Ina
rapidlyevolvingarealikeImagingitislikelythatnewareaswillappearinaveryshorttime
and should beadded tothe handbook, as wellas recent development enforce modifica-
tionsofexistingcontributions.Wearecommittedtoissuingperiodicupdatesandwelook
forwardtothefeedbackfromthecommunity.
OtmarScherzer
ComputationalScienceCenter
UniversityofVienna,Austria
and
RICAM
AustrianAcademyofSciences
Linz,Austria

Table of Contents
Preface................................................................................................... v
AbouttheEditor...................................................................................... xi
ListofContributors.................................................................................. xiii
Volume
InverseProblems–Methods
 LinearInverseProblems............................................................ 
CharlesGroetsch
 Large-ScaleInverseProblemsinImaging..................................... 
JulianneChung⋅SarahKnepper⋅JamesG.Nagy
 RegularizationMethodsforIll-PosedProblems............................ 
JinCheng⋅BerndHofmann
 DistanceMeasuresandApplicationstoMulti-Modal
VariationalImaging................................................................. 
ChristianePöschl⋅OtmarScherzer
 EnergyMinimizationMethods................................................... 
MilaNikolova
 CompressiveSensing............................................................... 
MassimoFornasier⋅HolgerRauhut
 DualityandConvexProgramming.............................................. 
JonathanM.Borwein⋅D.RussellLuke
 EMAlgorithms........................................................................ 
CharlesByrne⋅PaulP.B.Eggermont
 IterativeSolutionMethods........................................................ 
MartinBurger⋅BarbaraKaltenbacher⋅AndreasNeubauer
 LevelSetMethodsforStructuralInversionandImage
Reconstruction........................................................................ 
OliverDorn⋅DominiqueLesselier
viii TableofContents
Volume
InverseProblems–CaseExamples
 ExpansionMethods.................................................................. 
HabibAmmari⋅HyeonbaeKang
 SamplingMethods................................................................... 
MartinHanke⋅AndreasKirsch
 InverseScattering.................................................................... 
DavidColton⋅RainerKress
 ElectricalImpedanceTomography.............................................. 
AndyAdler⋅RominaGaburro·WilliamLionheart
 SyntheticApertureRadarImaging.............................................. 
MargaretCheney⋅BrettBorden
 Tomography........................................................................... 
GaborT.Herman
 OpticalImaging....................................................................... 
SimonR.Arridge⋅JariP.Kaipio·VilleKolehmainen⋅TanjaTarvainen
 PhotoacousticandThermoacousticTomography:
ImageFormationPrinciples....................................................... 
KunWang⋅MarkA.Anastasio
 MathematicsofPhotoacousticandThermoacousticTomography.... 
PeterKuchment⋅LeonidKunyansky
 WavePhenomena.................................................................... 
MattiLassas⋅MikkoSalo⋅GuntherUhlmann
Volume
ImageRestorationandAnalysis
 StatisticalMethodsinImaging................................................... 
DanielaCalvetti⋅ErkkiSomersalo
 SupervisedLearningbySupportVectorMachines........................ 
GabrieleSteidl
TableofContents ix
 TotalVariationinImaging......................................................... 
V.Caselles⋅A.Chambolle⋅M.Novaga
 NumericalMethodsandApplicationsinTotalVariationImage
Restoration.............................................................................
RaymondChan⋅TonyChan⋅AndyYip
 MumfordandShahModelanditsApplicationstoImage
SegmentationandImageRestoration.........................................
LeahBar⋅TonyF.Chan⋅GinmoChung⋅MiyounJung⋅NahumKiryati⋅
RamiMohieddine⋅NirSochen⋅LuminitaA.Vese
 LocalSmoothingNeighborhoodFilters....................................... 
Jean-MichelMorel⋅AntoniBuades⋅TomeuColl
 NeighborhoodFiltersandtheRecoveryofDInformation............. 
JulieDigne⋅MariellaDimiccoli⋅PhilippeSalembier⋅NeusSabater
 SplinesandMultiresolutionAnalysis.......................................... 
BrigitteForster
 GaborAnalysisforImaging....................................................... 
OleChristensen⋅HansG.Feichtinger⋅StephanPaukner
 ShapeSpaces..........................................................................
AlainTrouvé⋅LaurentYounes
 VariationalMethodsinShapeAnalysis........................................
MartinRumpf⋅BenediktWirth
 ManifoldIntrinsicSimilarity......................................................
AlexanderM.Bronstein⋅MichaelM.Bronstein
 ImageSegmentationwithShapePriors:ExplicitVersusImplicit
Representations...................................................................... 
DanielCremers
 StarletTransforminAstronomicalDataProcessing.......................
Jean-LucStarck⋅FionnMurtagh⋅MarioBertero
 DifferentialMethodsforMulti-DimensionalVisualDataAnalysis.....
WernerBenger⋅RenéHeinzl⋅DietmarHildenbrand⋅TinoWeinkauf⋅
HolgerTheisel⋅DavidTschumperlé
Index..................................................................................................... 