title: Tight Graph Framelets for Sparse Diffusion MRIq-Space Representation.
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 inq-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, inq-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 calltight graph framelets, in two specific applications: denoising and super-resolution inq-space using ℓ0regularization. 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.
authors.affiliation: Department of Radiology and BRIC, University of North Carolina, Chapel Hill, U.S.A.
authors.forename: Pew-Thian
authors.initials: PT
authors.lastname: Yap
authors.affiliation: Beijing International Center for Mathematical Research, Peking University, Beijing, China.
authors.forename: Bin
authors.initials: B
authors.lastname: Dong
authors.affiliation: Department of Psychiatry & Behavioral Sciences, Stanford University, U.S.A.
authors.forename: Yong
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Department of Radiology and BRIC, University of North Carolina, Chapel Hill, U.S.A.
authors.forename: Dinggang
authors.initials: D
authors.lastname: Shen
mesh_terms: D000465:Algorithms; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D058067:Wavelet Analysis