Tight graph framelets for sparse diffusion MRI q-space representation

Pew Thian Yap, Bin Dong, Yong Zhang, Dinggang Shen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)


In diffusion MRI,the outcome of estimation problems can often be improved by taking into account the correlation of diffusionweighted 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 quasiaffine 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 l0 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.

Original languageEnglish
Title of host publicationMedical Image Computing and Computer-Assisted Intervention - MICCAI 2016 - 19th International Conference, Proceedings
EditorsLeo Joskowicz, Mert R. Sabuncu, William Wells, Gozde Unal, Sebastian Ourselin
PublisherSpringer Verlag
Number of pages9
ISBN (Print)9783319467252
Publication statusPublished - 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9902 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2016.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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