SmoothingWfieldsWofWweightedWcollectionsWwithWapplicationsWtoWdiffusionWMRIWprocessing

GunnarWA.WSigurdssonWandWJerryWL.WPrince

Motivation

PriorWWork

Approach

Acknowledgements

References

Results

This8research8was8supported8in8part8by8Y”“8grants8R-CYS-Dk(-F8and8RPCYS-EPEzCM

ImageWAnalysisWandWCommunicationsWLab,WElectricalWandWComputerWEngineering,WJohnsWHopkinsWUniversity,WBaltimore,WMD,WUSA

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86 IN TRODUCT ION

Over the past dozen years5 many methods to reconst ruct neuronal fiber t racts in human white mat ter fromdi usion MRI data have been protocols the opportunity to exploit mult iple direct ions and their fract ionalcont ribut ions—generically referred to as multiGtensor models85 H—within each voxel have been developed6( here6

One way to address noise in di usion MRI data is to smooth the raw adapt ive anisot ropic noise filteringmethod of Sijbers et al6) in their MICCAI fiber cup challenge al6k used a nonlocal means approach5 andMcGraw et al6q used an image restorat ion approach specified by a variat ional formulat ion6 Another point atwhich to carry out smoothing is after tensor reconst ruct ion6 For example5 Tabelow et al6B and Chen et al6E

developed di erent approaches to smooth tensor fields6 However5 neither method generalizes to mult iGtensormodels or other representat ions specifying mult iple orientat ions at each voxel6 Although the smoothing of rawdata can certainly becarried out in mult iGtensor and mult iGorientat ion models Ssince it applies before theanalysisphasej5 the smoothing of mult iGtensor or mult iGorientat ion fields remains an open problem6

In this work we present a method to spat ially smooth an orientat ion field that has been est imated from theraw Sor smoothedj di usion MRI data6 The method considers both mult iple orientat ions and their fract ionalcont ribut ions—i6e65 their memberships—within each voxel6 In order to smooth between voxels5 a correspondenceof orientat ions between each pair of voxels is first solved6 A unique aspect of the present work is that a fuzzycorrespondence that involves both the collect ion of orientat ions and their fract ional cont ribut ions is producedby solving an opt imizat ion criterion6 In this way5 smoothing is carried out between populat ions that are likelyto be associated with each other while erroneous orientat ion associat ions are avoided6 Benefits of this approachare demonst rated on simulated phantom and in vivo data6

REFERENCES

[C] Peled] SM] Oriman] OM] – olesz] O M] and Westin] UMKO M] “Jeometrically constrained twoKtensor model for crossing tractsin dwi]” ¨agnetic resonance imaging H),zj] CPk(–CPF- ,P--kjM

[P] ’andman] B M qM] Bogovic] – M qM] Wan] “M] VlShahaby] O M VM ZM] Bazin] PMK’M] and Prince] – M ’M] “Resolution of crossingfibers with constrained compressed sensing using diffusion tensor mri]” Yeuro”mage Dz,(j] PCFD–PCEk ,P-CPjM

[(] Zreher] B M] Schneider] – M] ¨ader] ”M] ¨artin] VM] “ennig] – M] and ”l’yasov] ZM] “¨ultitensor approach for analysis andtracking of complex fiber configurations]” ¨agnetic resonance in medicine D),Dj] CPCk–CPPD ,P--DjM

[)] Sijbers] – M] den /ekker] qM – M] Van der ’inden] qM] Verhoye] ¨M] and Van /yck] /M] “qdaptive anisotropic noisefiltering for magnitude mr data]” ¨agnetic resonance imaging CF,C-j] CD((–CD(z ,CzzzjM

[D] Zuurstra] qM] /olui] SM] and ¨ichailovich] OM] ““ardi denoising using nonlocal means on sP]” in [SP”V ¨edical”maging]] E(C)-”–E(C)-”] ”nternational Society for Optics and Photonics ,P-CPjM

[k] ¨cJraw] T M] Vemuri] B M]¨Ozarslan] VM] Uhen] YM] and ¨areci] T M] “Variational denoising of diffusion weighted mri]””nverse Problems and ”maging (k,)j] kPD ,P--zjM

[F] Tabelow] ZM] Polzehl] – M] Spokoiny] VM] and Voss] “M UM] “/iffusion tensor imagingv Structural adaptive smoothing]”Yeuro”mage ([,)j] CFk(–CFF( ,P--EjM

[E] Uhen] B M and “su] VM WM] “Yoise removal in magnetic resonance diffusion tensor imaging]” ¨agnetic Resonance in¨edicine D),Pj] (z(–)-C ,P--DjM

Algorithm

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