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A Bregman iteration algorithm for shearlet-regularized compressed sensing in MRI

Jan Aelterman (UGent)
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Abstract
Recently, it has been shown that MRI acquisition can be improved a lot using Compressive Sensing (CS) techniques. In our workwe focus on reconstructing sub-Nyquist sampled MRI data, which we regularize using the shearlet transform. The shearlet transform is credited as providing an optimally sparse frame for representing smooth image regions delineated by edges. Hence, it is a good model for MRI images. The resulting basis pursuit (BP) CS formulation is solved using split Bregman iteration, which splits the BP problem into several easier subproblems. The resulting algorithm allows an exact, parameter-free solution to the constrained BP problem. The results show that the algorithm is able to perform any MRI reconstruction task (sub-Nyquist sampled data or not) and even perform image fusion and resolution enhancement.

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Chicago
Aelterman, Jan. 2010. “A Bregman Iteration Algorithm for Shearlet-regularized Compressed Sensing in MRI.” In Sparsity and Modern Mathematical Methods for High Dimensional Data, 11–11. Brussels, Belgium: Vrije Universiteit Brussel (VUB).
APA
Aelterman, J. (2010). A Bregman iteration algorithm for shearlet-regularized compressed sensing in MRI. Sparsity and modern mathematical methods for high dimensional data (pp. 11–11). Presented at the Interdisciplinary workshop on Sparsity and Modern Mathematical Methods for High Dimensional Data, Brussels, Belgium: Vrije Universiteit Brussel (VUB).
Vancouver
1.
Aelterman J. A Bregman iteration algorithm for shearlet-regularized compressed sensing in MRI. Sparsity and modern mathematical methods for high dimensional data. Brussels, Belgium: Vrije Universiteit Brussel (VUB); 2010. p. 11–11.
MLA
Aelterman, Jan. “A Bregman Iteration Algorithm for Shearlet-regularized Compressed Sensing in MRI.” Sparsity and Modern Mathematical Methods for High Dimensional Data. Brussels, Belgium: Vrije Universiteit Brussel (VUB), 2010. 11–11. Print.
@inproceedings{1941341,
  abstract     = {Recently, it has been shown that MRI acquisition can be improved a lot using Compressive Sensing (CS) techniques. In our workwe focus on reconstructing sub-Nyquist sampled MRI data, which we regularize using the shearlet transform. The shearlet transform is credited as providing an optimally sparse frame for representing smooth image regions delineated by edges. Hence, it is a good model for MRI images. The resulting basis pursuit (BP) CS formulation is solved using split Bregman iteration, which splits the BP problem into several easier subproblems. The resulting algorithm allows an exact, parameter-free solution to the constrained BP problem. The results show that the algorithm is able to perform any MRI reconstruction task (sub-Nyquist sampled data or not) and even perform image fusion and resolution enhancement.},
  author       = {Aelterman, Jan},
  booktitle    = {Sparsity and modern mathematical methods for high dimensional data},
  language     = {eng},
  location     = {Brussels, Belgium},
  pages        = {11--11},
  publisher    = {Vrije Universiteit Brussel (VUB)},
  title        = {A Bregman iteration algorithm for shearlet-regularized compressed sensing in MRI},
  year         = {2010},
}