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

Jan Aelterman UGent (2010) Sparsity and modern mathematical methods for high dimensional data. p.11-11
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.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
in
Sparsity and modern mathematical methods for high dimensional data
pages
11 - 11
publisher
Vrije Universiteit Brussel (VUB)
place of publication
Brussels, Belgium
conference name
Interdisciplinary workshop on Sparsity and Modern Mathematical Methods for High Dimensional Data
conference location
Brussels, Belgium
conference start
2010-04-06
conference end
2010-04-10
language
English
UGent publication?
yes
classification
C3
copyright statement
I have transferred the copyright for this publication to the publisher
id
1941341
handle
http://hdl.handle.net/1854/LU-1941341
date created
2011-11-10 10:47:22
date last changed
2017-01-02 09:53:20
@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},
}

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.