Tight Graph Framelets for Sparse Diffusion MRI q-Space Representation

  • Pew-Thian YapEmail author
  • Bin Dong
  • Yong Zhang
  • Dinggang Shen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9902)


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.


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Authors and Affiliations

  • Pew-Thian Yap
    • 1
    Email author
  • Bin Dong
    • 2
  • Yong Zhang
    • 3
  • Dinggang Shen
    • 1
  1. 1.Department of Radiology and BRICUniversity of North CarolinaChapel HillUSA
  2. 2.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina
  3. 3.Department of Psychiatry and Behavioral SciencesStanford UniversityStanfordUSA

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