Tight Graph Framelets for Sparse Diffusion MRI q-Space Representation

详细信息    查看全文

• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9902
• 期：1
• 页码：561-569
• 全文大小：493 KB
• 参考文献：1.Dong, B.: Sparse representation on graphs by tight wavelet frames and applications. Applied and Computational Harmonic Analysis (2015)
  2.Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmonic Anal. 30(2), 129–150 (2011)MathSciNet CrossRef MATH
  3.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)MathSciNet CrossRef MATH
  4.Michailovich, O., Rathi, Y.: On approximation of orientation distributions by means of spherical ridgelets. IEEE Trans. Image Process. 19(2), 461–476 (2010)MathSciNet CrossRef
  5.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)MathSciNet CrossRef MATH
  6.Zhang, Y., Dong, B., Lu, Z.: \(\ell _{0}\) minimization for wavelet frame based image restoration. Math. Comput. 82, 995–1015 (2013)MathSciNet CrossRef MATH
  7.Tuch, D.S.: Q-ball imaging. Magn. Reson. Med. 52, 1358–1372 (2004)CrossRef
  8.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
  9.Lu, Z., Zhang, Y.: Sparse approximation via penalty decomposition methods. SIAM J. Optim. 23(4), 2448–2478 (2013)MathSciNet CrossRef MATH
  10.Lu, Z.: Iterative hard thresholding methods for \(l_0\) regularized convex cone programming. Math. Prog. Ser. A B 147(1–2), 125–154 (2014)CrossRef MATH
  11.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_​23 CrossRef
  12.Donoho, D.L.: De-noising by soft-thresholding. IEEE Trans. Inf. Theor. 41(3), 613–627 (1995)MathSciNet CrossRef MATH
  13.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
  
• 作者单位：Pew-Thian Yap (18)
  Bin Dong (19)
  Yong Zhang (20)
  Dinggang Shen (18)
  
  18. Department of Radiology and BRIC, University of North Carolina, Chapel Hill, USA
  19. Beijing International Center for Mathematical Research, Peking University, Beijing, China
  20. Department of Psychiatry and Behavioral Sciences, Stanford University, Stanford, USA
  
• 丛书名：Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2016
• ISBN：978-3-319-46726-9
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9902

文摘

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.