Skip to main content

2016 | OriginalPaper | Buchkapitel

Tight Graph Framelets for Sparse Diffusion MRI q-Space Representation

verfasst von : Pew-Thian Yap, Bin Dong, Yong Zhang, Dinggang Shen

Erschienen in: Medical Image Computing and Computer-Assisted Intervention - MICCAI 2016

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In diffusion MRI, the outcome of estimation problems can often be improved by taking into account the correlation of diffusion-weighted images scanned with neighboring wavevectors in q-space. For this purpose, we propose in this paper to employ tight wavelet frames constructed on non-flat domains for multi-scale sparse representation of diffusion signals. This representation is well suited for signals sampled regularly or irregularly, such as on a grid or on multiple shells, in q-space. Using spectral graph theory, the frames are constructed based on quasi-affine systems (i.e., generalized dilations and shifts of a finite collection of wavelet functions) defined on graphs, which can be seen as a discrete representation of manifolds. The associated wavelet analysis and synthesis transforms can be computed efficiently and accurately without the need for explicit eigen-decomposition of the graph Laplacian, allowing scalability to very large problems. We demonstrate the effectiveness of this representation, generated using what we call tight graph framelets, in two specific applications: denoising and super-resolution in q-space using \(\ell _{0}\) regularization. The associated optimization problem involves only thresholding and solving a trivial inverse problem in an iterative manner. The effectiveness of graph framelets is confirmed via evaluation using synthetic data with noncentral chi noise and real data with repeated scans.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Dong, B.: Sparse representation on graphs by tight wavelet frames and applications. Applied and Computational Harmonic Analysis (2015) Dong, B.: Sparse representation on graphs by tight wavelet frames and applications. Applied and Computational Harmonic Analysis (2015)
2.
Zurück zum Zitat Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmonic Anal. 30(2), 129–150 (2011)MathSciNetCrossRefMATH Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmonic Anal. 30(2), 129–150 (2011)MathSciNetCrossRefMATH
3.
Zurück zum Zitat Ron, A., Shen, Z.: Affine systems in \(L_{2}(\mathbb{R}^{d})\): the analysis of the analysis operator. J. Funct. Anal. 148(2), 408–447 (1997)MathSciNetCrossRefMATH Ron, A., Shen, Z.: Affine systems in \(L_{2}(\mathbb{R}^{d})\): the analysis of the analysis operator. J. Funct. Anal. 148(2), 408–447 (1997)MathSciNetCrossRefMATH
4.
Zurück zum Zitat Michailovich, O., Rathi, Y.: On approximation of orientation distributions by means of spherical ridgelets. IEEE Trans. Image Process. 19(2), 461–476 (2010)MathSciNetCrossRefMATH Michailovich, O., Rathi, Y.: On approximation of orientation distributions by means of spherical ridgelets. IEEE Trans. Image Process. 19(2), 461–476 (2010)MathSciNetCrossRefMATH
5.
Zurück zum Zitat Chan, R.H., Chan, T.F., Shen, L., Shen, Z.: Wavelet algorithms for high-resolution image reconstruction. SIAM J. Sci. Comput. 24(4), 1408–1432 (2003)MathSciNetCrossRefMATH Chan, R.H., Chan, T.F., Shen, L., Shen, Z.: Wavelet algorithms for high-resolution image reconstruction. SIAM J. Sci. Comput. 24(4), 1408–1432 (2003)MathSciNetCrossRefMATH
6.
Zurück zum Zitat Zhang, Y., Dong, B., Lu, Z.: \(\ell _{0}\) minimization for wavelet frame based image restoration. Math. Comput. 82, 995–1015 (2013)MathSciNetCrossRefMATH Zhang, Y., Dong, B., Lu, Z.: \(\ell _{0}\) minimization for wavelet frame based image restoration. Math. Comput. 82, 995–1015 (2013)MathSciNetCrossRefMATH
7.
8.
Zurück zum Zitat Belkin, M., Niyogi, P.: Towards a theoretical foundation for laplacian-based manifold methods. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, pp. 486–500. Springer, Heidelberg (2005)CrossRef Belkin, M., Niyogi, P.: Towards a theoretical foundation for laplacian-based manifold methods. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, pp. 486–500. Springer, Heidelberg (2005)CrossRef
10.
Zurück zum Zitat Lu, Z.: Iterative hard thresholding methods for \(l_0\) regularized convex cone programming. Math. Prog. Ser. A B 147(1–2), 125–154 (2014)MathSciNetCrossRefMATH Lu, Z.: Iterative hard thresholding methods for \(l_0\) regularized convex cone programming. Math. Prog. Ser. A B 147(1–2), 125–154 (2014)MathSciNetCrossRefMATH
11.
Zurück zum Zitat Yap, P.-T., Zhang, Y., Shen, D.: Diffusion compartmentalization using response function groups with cardinality penalization. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9349, pp. 183–190. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24553-9_23CrossRef Yap, P.-T., Zhang, Y., Shen, D.: Diffusion compartmentalization using response function groups with cardinality penalization. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9349, pp. 183–190. Springer, Heidelberg (2015). doi:10.​1007/​978-3-319-24553-9_​23CrossRef
13.
Zurück zum Zitat Koay, C.G., Özarslan, E., Basser, P.J.: A signal transformational framework for breaking the noise floor and its applications in MRI. J. Magn. Reson. 197, 108–119 (2009)CrossRef Koay, C.G., Özarslan, E., Basser, P.J.: A signal transformational framework for breaking the noise floor and its applications in MRI. J. Magn. Reson. 197, 108–119 (2009)CrossRef
Metadaten
Titel
Tight Graph Framelets for Sparse Diffusion MRI q-Space Representation
verfasst von
Pew-Thian Yap
Bin Dong
Yong Zhang
Dinggang Shen
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-46726-9_65