Chapter title |
Tight Graph Framelets for Sparse Diffusion MRI q-Space Representation
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Chapter number | 65 |
Book title |
Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2016
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Published in |
Lecture notes in computer science, October 2016
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DOI | 10.1007/978-3-319-46726-9_65 |
Pubmed ID | |
Book ISBNs |
978-3-31-946725-2, 978-3-31-946726-9
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Authors |
Pew-Thian Yap, Bin Dong, Yong Zhang, Dinggang Shen, Yap, Pew-Thian, Dong, Bin, Zhang, Yong, Shen, Dinggang |
Editors |
Sebastien Ourselin, Leo Joskowicz, Mert R. Sabuncu, Gozde Unal, William Wells |
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 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. |
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