TY - GEN
T1 - Tight graph framelets for sparse diffusion MRI q-space representation
AU - Yap, Pew Thian
AU - Dong, Bin
AU - Zhang, Yong
AU - Shen, Dinggang
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-319-46726-9_65
DO - 10.1007/978-3-319-46726-9_65
M3 - Conference contribution
AN - SCOPUS:84996565512
SN - 9783319467252
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 561
EP - 569
BT - Medical Image Computing and Computer-Assisted Intervention - MICCAI 2016 - 19th International Conference, Proceedings
A2 - Joskowicz, Leo
A2 - Sabuncu, Mert R.
A2 - Wells, William
A2 - Unal, Gozde
A2 - Ourselin, Sebastian
PB - Springer Verlag
ER -