Skip to main content

Locally Weighted Regression for Estimating and Smoothing ODF Field Simultaneously

  • Conference paper
Medical Imaging and Augmented Reality (MIAR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6326))

Included in the following conference series:

Abstract

High angular resolution diffusion imaging (HARDI) has become an important tool for resolving neural architecture in regions with complex patterns of fiber crossing. A popular method for estimating the diffusion orientation distribution function (ODF) employs a least square (LS) approach by modeling the raw HARDI data on a spherical harmonic basis. We propose herein a novel approach for reconstruction of ODF fields from raw HARDI data that combines into one step the smoothing of raw HARDI data and the estimation of ODF field using correlated information in a local neighborhood. Based on the most popular method of least square for estimating ODF, we incorporated into it local weights that are determined by a special weighting function, making it a locally weighted linear least square method (LWLLS). The method thus can efficiently perform the smoothing of HARDI data and estimating the ODF field simultaneously. We evaluated the effectiveness of this method using both simulated and real-world HARDI data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basser, P., Mattiello, J., Le Bihan, D.: Estimation of the effective self-diffusion tensor from the NMR spin echo. Journal of Magnetic Resonance B 103, 247–254 (1994)

    Article  Google Scholar 

  2. Tuch, D.S.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magnetic Resonance in Medicine 48, 577–582 (2002)

    Article  Google Scholar 

  3. Tuch, D.S.: Q-ball imaging. Magnetic Resonance in Medicine 52(6), 1358–1372 (2004)

    Article  Google Scholar 

  4. Jansons, K.M., Alexander, D.C.: Persistent angular structure: new insights from diffusion magnetic resonance imaging data. Inverse Probl. 19, 1031–1046 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Tournier, J.D., Calamante, F., Connelly, A.: Robust determination of the fibre orientation distribution in diffusion MRI. NeuroImage 35(4), 1459–1472 (2007)

    Article  Google Scholar 

  6. Jian, B., Vemuri, B.: A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted MRI. IEEE TMI 26(11), 1464–1471 (2007)

    Google Scholar 

  7. Ozarslan, E., Shepherd, T., Vemuri, B.C., Blackband, S., Mareci, T.H.: Resolution of complex tissue micro architecture using the diffusion orientation transform (DOT). NeuroImage 31, 1086–1103 (2006)

    Article  Google Scholar 

  8. Tristán-Vega, A., Westin, C.-F., Aja-Fernández, S.: Estimation of fiber orientation probability density functions in high angular resolution diffusion imaging. NeuroImage 47(2), 638–650 (2009)

    Article  Google Scholar 

  9. Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast and robust analytical Q-ball imaging. Magnetic Resonance in Medicine 58, 497–510 (2007)

    Article  Google Scholar 

  10. Frank, L.R.: Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magnetic Resonance in Medicine 47(6), 1083–1099 (2002)

    Article  Google Scholar 

  11. Hess, C.P., Mukherjee, P., Han, E.T., Xu, D., Vigneron, D.B.: Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis. MRM 56(1) (2006)

    Google Scholar 

  12. Aganj, I., Lenglet, C., Sapiro, G.: ODF reconstruction in Q-ball imaging with solid angle consideration. In: IEEE Int. Symposium on Biomedical Imaging (2009)

    Google Scholar 

  13. Rathi, Y., Michailovich, O., Bouix, S., Shenton, M.: Orientation distribution estimation for Q-ball imaging. In: MMBIA (2008)

    Google Scholar 

  14. Michailovich, O., Rathi, Y.: On approximation of orientation distributions by means of spherical ridgelets. IEEE TIP 19(2), 461–477 (2010)

    Google Scholar 

  15. Assemlal, H.E., Tschumperl’e, D., Brun, L.: Robust variational estimation of PDF functions from Diffusion MR signal. In: CDMRI (2008)

    Google Scholar 

  16. Goh, A., Lenglet, C., Thompson, P., Vidal, R.: Estimating Orientation Distribution Functions with Probability Density Constraints and Spatial Regularity. In: Yang, G.-Z., et al. (eds.) MICCAI 2009, Part I. LNCS, vol. 5762, pp. 877–885. Springer, Heidelberg (2009)

    Google Scholar 

  17. Nadaraya, E.A.: On estimating regression Theory. Probab. Appl. 9(1), 141–142 (1964)

    Article  Google Scholar 

  18. Ruppert, D., Wand, M.P.: Multivariate locally weighted least squares regression. Ann. Statist. 22(3), 1346–1370 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: IEEE International Conference on Computer Vision (ICCV), pp. 839–846 (1998)

    Google Scholar 

  20. Dyrby, T., Baaré, W., Alexander, D.C., Jelsing, J., Garde, E., Søgaard, L.V.: An ex vivo imaging pipeline for producing high-quality and high-resolution diffusion-weighted imaging datasets. Human Brain Mapping (2010), doi:10.1002/hbm.21043

    Google Scholar 

  21. Tristán-Vega, A., Aja-Fernández, S.: DWI filtering using joint information for DTI and HARDI. Med. Image. Anal. 14(2), 205–218 (2010)

    Article  Google Scholar 

  22. Descoteaux, M., Wiest-Daesslé, N., Prima, S., Barillot, C., Deriche, R.: Impact of Rician Adapted Non-Local Means Filtering on HARDI. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 122–130. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liu, X., Yang, G., Peterson, B.S., Xu, D. (2010). Locally Weighted Regression for Estimating and Smoothing ODF Field Simultaneously. In: Liao, H., Edwards, P.J."., Pan, X., Fan, Y., Yang, GZ. (eds) Medical Imaging and Augmented Reality. MIAR 2010. Lecture Notes in Computer Science, vol 6326. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15699-1_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15699-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15698-4

  • Online ISBN: 978-3-642-15699-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics