Spatio-temporal wavelet regularization for parallel MRI reconstruction: application to functional MRI

  • Lotfi Chaari
  • Philippe Ciuciu
  • Sébastien Mériaux
  • Jean-Christophe Pesquet
Research Article



Parallel magnetic resonance imaging (MRI) is a fast imaging technique that helps acquiring highly resolved images in space/time. Its performance depends on the reconstruction algorithm, which can proceed either in the k-space or in the image domain.

Objective and methods

To improve the performance of the widely used SENSE algorithm, 2D regularization in the wavelet domain has been investigated. In this paper, we first extend this approach to 3D-wavelet representations and the 3D sparsity-promoting regularization term, in order to address reconstruction artifacts that propagate across adjacent slices. The resulting optimality criterion is convex but nonsmooth, and we resort to the parallel proximal algorithm to minimize it. Second, to account for temporal correlation between successive scans in functional MRI (fMRI), we extend our first contribution to 3D + \(t\) acquisition schemes by incorporating a prior along the time axis into the objective function.


Our first method (3D-UWR-SENSE) is validated on T1-MRI anatomical data for gray/white matter segmentation. The second method (4D-UWR-SENSE) is validated for detecting evoked activity during a fast event-related functional MRI protocol.


We show that our algorithm outperforms the SENSE reconstruction at the subject and group levels (15 subjects) for different contrasts of interest (motor or computation tasks) and two parallel acceleration factors (\(R=2\) and \(R=4\)) on \(2\times 2\times 3\,\hbox{mm}^3\) echo planar imaging (EPI) images.


Parallel MRI fMRI Wavelet transform Spatio-temporal regularization Convex optimization 



This work has been partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02. The work of Philippe Ciuciu was partially supported by the CIMI (Centre International de Mathmatiques et d’Informatique) Excellence program during the winter and spring of 2013.

Supplementary material


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Copyright information

© ESMRMB 2014

Authors and Affiliations

  • Lotfi Chaari
    • 1
  • Philippe Ciuciu
    • 2
    • 3
  • Sébastien Mériaux
    • 2
  • Jean-Christophe Pesquet
    • 4
  1. 1.IRIT-INP-ENSEEIHTUniversity of ToulouseToulouseFrance
  2. 2.CEA/NeuroSpinGif-sur-YvetteFrance
  3. 3.INRIA Saclay, ParietalSaclayFrance
  4. 4.LIGMUniversity Paris-EstMarne-la-ValléeFrance

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