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

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

Abstract

Background

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.

Results

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.

Conclusion

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.

Keywords

Parallel MRI fMRI Wavelet transform Spatio-temporal regularization Convex optimization 

References

  1. 1.
    Chaari L, Mériaux S, Badillo S, Ciuciu P, Pesquet JC (2011a) 3D wavelet-based regularization for parallel MRI reconstruction: impact on subject and group-level statistical sensitivity in fMRI. In: IEEE international symposium on biomedical imaging (ISBI). Chicago, USA, pp 460–464Google Scholar
  2. 2.
    Kochunov P, Rivière D, Lancaster JL, Mangin JF, Cointepas Y, Glahn D, Fox P, Rogers J (2005) Development of high-resolution MRI imaging and image processing for live and post-mortem primates. Human Brain Mapping (HBM). Canada, Toronto, pp 1–3Google Scholar
  3. 3.
    Rabrait C, Ciuciu P, Ribès A, Poupon C, Leroux P, Lebon V, Dehaene-Lambertz G, Bihan DL, Lethimonnier F (2008) High temporal resolution functional MRI using parallel echo volume imaging. Magn Reson Imaging 27:744–753CrossRefGoogle Scholar
  4. 4.
    Sodickson DK, Manning WJ (1997) Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med 38:591–603PubMedCrossRefGoogle Scholar
  5. 5.
    Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P (1999) SENSE: sensitivity encoding for fast MRI. Magn Reson Med 42:952–962PubMedCrossRefGoogle Scholar
  6. 6.
    Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A (2002) Generalized autocalibrating partially parallel acquisitions GRAPPA. Magn Reson Med 47:1202–1210PubMedCrossRefGoogle Scholar
  7. 7.
    Candès E, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52:489–509CrossRefGoogle Scholar
  8. 8.
    Lustig M, Donoho D, Pauly JM (2007) Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 58:1182–1195PubMedCrossRefGoogle Scholar
  9. 9.
    Bilgin A, Trouard TP, Gmitro AF, Altbach MI (2008) Randomly perturbed radial trajectories for compressed sensing MRI. In: Meeting of the international society for magnetic resonance in medicine. Toronto, Canada, p 3152Google Scholar
  10. 10.
    Yang A, Feng L, Xu J, Selesnick I, Sodickson D K, Otazo R (2012) Improved compressed sensing reconstruction with overcomplete wavelet transforms. In: Meeting of the international society for magnetic resonance in medicine, Melbourne, Australia, p 3769Google Scholar
  11. 11.
    Holland DJ, Liu C, Song X, Mazerolle EL, Stevens MT, Sederman AJ, Gladden LF, D’Arcy RCN, Bowen CV, Beyea SD (2013) Compressed sensing reconstruction improves sensitivity of variable density spiral fMRI. Magn Reson Med 70:1634–1643PubMedCrossRefGoogle Scholar
  12. 12.
    Liang D, Liu B, Wang J, Ying L (2009) Accelerating SENSE using compressed sensing. Magn Reson Med 62:1574–84PubMedCrossRefGoogle Scholar
  13. 13.
    Boyer C, Ciuciu P, Weiss P, Mériaux S (2012) HYR\(^2\)PICS: Hybrid regularized reconstruction for combined parallel imaging and compressive sensing in MRI. In: 9th international symposium on biomedical imaging (ISBI). Barcelona, Spain, pp 66–69Google Scholar
  14. 14.
    Madore B, Glover GH, Pelc NJ (1999) Unaliasing by Fourier-encoding the overlaps using the temporal dimension (UNFOLD), applied to cardiac imaging and fMRI. Magn Reson Med 42:813–828PubMedCrossRefGoogle Scholar
  15. 15.
    Tsao J, Boesiger P, Pruessmann KP (2003) k-t BLAST and k-t SENSE: dynamic MRI with high frame rate exploiting spatiotemporal correlations. Magn Reson Med 50:1031–1042PubMedCrossRefGoogle Scholar
  16. 16.
    Lustig M, Santos JM, Donoho DL, Pauly JM (2001) k-t SPARSE: high frame rate dynamic MRI exploiting spatio-temporal sparsity. In: International society for magnetic resonance in medicine. Washington, USA, p 2420Google Scholar
  17. 17.
    Wang J, Kluge T, Nittka M, Jellus V, Kuhn B, Kiefer B (2001) Parallel acquisition techniques with modified SENSE reconstruction mSENSE. In: 1st Wuzburg workshop on parallel imaging basics and clinical applications. Wuzburg, Germany, p 92Google Scholar
  18. 18.
    Tsao J, Kozerke S, Boesiger P, Pruessmann KP (2005) Optimizing spatiotemporal sampling for k-t BLAST and k-t SENSE: application to high-resolution real-time cardiac steady-state free precession. Magn Reson Med 53:1372–1382PubMedCrossRefGoogle Scholar
  19. 19.
    Huang F, Akao J, Vijayakumar S, Duensing GR, Limkeman M (2005) k-t GRAPPA: a k-space implementation for dynamic MRI with high reduction factor. Magn Reson Med 54:1172–1184PubMedCrossRefGoogle Scholar
  20. 20.
    Jung H, Ye JC, Kim EY (2007) Improved k-t BLAST and k-t SENSE using FOCUSS. Phys Med Biol 52:3201–3226PubMedCrossRefGoogle Scholar
  21. 21.
    Jung H, Sung K, Nayak KS, Kim EY, Ye JC (2009) k-t FOCUSS: a general compressed sensing framework for high resolution dynamic MRI. Magn Reson Med 61:103–116PubMedCrossRefGoogle Scholar
  22. 22.
    Damoiseaux JS, Rombouts SA, Barkhof F, Scheltens P, Stam CJ, Smith SM, Beckmann CF (2006) Consistent resting-state networks across healthy subjects. Proc Natl Acad Sci USA 103:13848–1385PubMedCentralPubMedCrossRefGoogle Scholar
  23. 23.
    Dale AM (1999) Optimal experimental design for event-related fMRI. Hum Brain Mapp 8:109–114PubMedCrossRefGoogle Scholar
  24. 24.
    Varoquaux G, Sadaghiani S, Pinel P, Kleinschmidt A, Poline JB, Thirion B (2010) A group model for stable multi-subject ICA on fMRI datasets. Neuroimage 51:288–299PubMedCrossRefGoogle Scholar
  25. 25.
    Ciuciu P, Varoquaux G, Abry P, Sadaghiani S, Kleinschmidt A (2012) Scale-free and multifractal time dynamics of fMRI signals during rest and task. Front Physiol 3:1–18CrossRefGoogle Scholar
  26. 26.
    Birn R, Cox R, Bandettini PA (2002) Detection versus estimation in event-related fMRI: choosing the optimal stimulus timing. Neuroimage 15:252–264PubMedCrossRefGoogle Scholar
  27. 27.
    Logothetis NK (2008) What we can do and what we cannot do with fMRI. Nature 453:869–878PubMedCrossRefGoogle Scholar
  28. 28.
    de Zwart J, Gelderen PV, Kellman P, Duyn JH (2002) Application of sensitivity-encoded echo-planar imaging for blood oxygen level-dependent functional brain imaging. Magn Reson Med 48:1011–1020PubMedCrossRefGoogle Scholar
  29. 29.
    Preibisch C (2003) Functional MRI using sensitivity-encoded echo planar imaging (SENSE-EPI). Neuroimage 19:412–421PubMedCrossRefGoogle Scholar
  30. 30.
    de Zwart J, Gelderen PV, Golay X, Ikonomidou VN, Duyn JH (2006) Accelerated parallel imaging for functional imaging of the human brain. NMR Biomed 19:342–351PubMedCrossRefGoogle Scholar
  31. 31.
    Utting JF, Kozerke S, Schnitker R, Niendorf T (2010) Comparison of k-t SENSE/k-t BLAST with conventional SENSE applied to BOLD fMRI. J Magn Reson Imaging 32:235–241PubMedCrossRefGoogle Scholar
  32. 32.
    Liang ZP, Bammer R, Ji J, Pelc NJ, Glover GH (2002) Making better SENSE: wavelet denoising, Tikhonov regularization, and total least squares. In: International society for magnetic resonance in medicine. Hawaï, USA, p 2388Google Scholar
  33. 33.
    Ying L, Xu D, Liang ZP (2004) On Tikhonov regularization for image reconstruction in parallel MRI. In: IEEE engineering in medicine and biology society. San Francisco, USA, pp 1056–1059Google Scholar
  34. 34.
    Zou YM, Ying L, Liu B (2008) SparseSENSE: application of compressed sensing in parallel MRI. In: IEEE international conference on technology and applications in biomedicine. Shenzhen, China, pp 127–130 Google Scholar
  35. 35.
    Chaari L, Pesquet JC, Benazza-Benyahia A, Ciuciu P (2008) Autocalibrated parallel MRI reconstruction in the wavelet domain. In: IEEE international symposium on biomedical imaging (ISBI). Paris, France, pp 756–759Google Scholar
  36. 36.
    Liu B, Abdelsalam E, Sheng J, Ying L (2008a) Improved spiral SENSE reconstruction using a multiscale wavelet model. In: IEEE international symposium on biomedical imaging (ISBI). Paris, France, pp 1505–1508Google Scholar
  37. 37.
    Chaari L, Pesquet JC, Benazza-Benyahia A, Ciuciu P (2011b) A wavelet-based regularized reconstruction algorithm for SENSE parallel MRI with applications to neuroimaging. Med Image Anal 15:185–2010PubMedCrossRefGoogle Scholar
  38. 38.
    Chaari L, Mériaux S, Pesquet JC, Ciuciu P (2010a) Impact of the parallel imaging reconstruction algorithm on brain activity detection in fMRI. In: International symposium on applied sciences in biomedical and communication technologies (ISABEL). Italy, Rome, pp 1–5Google Scholar
  39. 39.
    Jakob P, Griswold M, Breuer F, Blaimer M, Seiberlich N (2006) A 3D GRAPPA algorithm for volumetric parallel imaging. In: Scientific meeting international society for magnetic resonance in medicine, Seattle, USA, p 286Google Scholar
  40. 40.
    Aguirre GK, Zarahn E, D’Esposito M (1997) Empirical analysis of BOLD fMRI statistics. II. Spatially smoothed data collected under null-hypothesis and experimental conditions. Neuroimage 5:199–212PubMedCrossRefGoogle Scholar
  41. 41.
    Zarahn E, Aguirre GK, D’Esposito M (1997) Empirical analysis of BOLD fMRI statistics. I. Spatially unsmoothed data collected under null-hypothesis conditions. Neuroimage 5:179–197PubMedCrossRefGoogle Scholar
  42. 42.
    Purdon PL, Weisskoff RM (1998) Effect of temporal autocorrelation due to physiological noise and stimulus paradigm on voxel-level false-positive rates in fMRI. Hum Brain Mapp 6:239–249PubMedCrossRefGoogle Scholar
  43. 43.
    Woolrich M, Ripley B, Brady M, Smith S (2001) Temporal autocorrelation in univariate linear modelling of fMRI data. Neuroimage 14:1370–1386PubMedCrossRefGoogle Scholar
  44. 44.
    Worsley KJ, Liao CH, Aston J, Petre V, Duncan GH, Morales F, Evans AC (2002) A general statistical analysis for fMRI data. Neuroimage 15:1–15PubMedCrossRefGoogle Scholar
  45. 45.
    Penny WD, Kiebel S, Friston KJ (2003) Variational Bayesian inference for fMRI time series. Neuroimage 19:727–741PubMedCrossRefGoogle Scholar
  46. 46.
    Chaari L, Vincent T, Forbes F, Dojat M, Ciuciu P (2013) Fast joint detection-estimation of evoked brain activity in event-related fMRI using a variational approach. IEEE Trans Med Imaging 32:821–837PubMedCentralPubMedCrossRefGoogle Scholar
  47. 47.
    Combettes PL, Pesquet JC (2008) A proximal decomposition method for solving convex variational inverse problems. Inverse Probl 24:27CrossRefGoogle Scholar
  48. 48.
    Sodickson DK (2000) Tailored SMASH image reconstructions for robust in vivo parallel MR imaging. Magn Reson Med 44:243–251PubMedCrossRefGoogle Scholar
  49. 49.
    Keeling SL (2003) Total variation based convex filters for medical imaging. Appl Math Comput 139:101–1195CrossRefGoogle Scholar
  50. 50.
    Liu B, King K, Steckner M, Xie J, Sheng J, Ying L (2008b) Regularized sensitivity encoding (SENSE) reconstruction using Bregman iterations. Magn Reson Med 61:145–152CrossRefGoogle Scholar
  51. 51.
    Guerquin-Kern M, Haberlin M, Pruessmann KP, Unser M (2011) A fast wavelet-based reconstruction method for magnetic resonance imaging. IEEE Trans Med Imaging 30:1649–1660PubMedCrossRefGoogle Scholar
  52. 52.
    Sümbül U, Santos JM, Pauly JM (2009) Improved time series reconstruction for dynamic magnetic resonance imaging. IEEE Trans Med Imaging 28:1093–1104PubMedCentralPubMedCrossRefGoogle Scholar
  53. 53.
    Pinel P, Thirion B, Mériaux S, Jobert A, Serres J, Le Bihan D, Poline JB, Dehaene S (2007) Fast reproducible identification and large-scale databasing of individual functional cognitive networks. BMC Neurosci 8:1–18CrossRefGoogle Scholar
  54. 54.
    Daubechies I (1992) Ten lectures on wavelets. In: Society for industrial and applied mathematics. PhiladelphiaGoogle Scholar
  55. 55.
    Dehaene S (1999) Cerebral bases of number processing and calculation. In: Gazzaniga M (ed) The new cognitive neurosciences, chap 68. MIT Press, Cambridge, pp 987–998Google Scholar
  56. 56.
    Nichols TE, Hayasaka S (2003) Controlling the familywise error rate in functional neuroimaging: a comparative review. Stat Methods Med Res 12:419–446PubMedCrossRefGoogle Scholar
  57. 57.
    Brett M, Penny W, Kiebel S (2004) Introduction to random field theory. In: Frackowiak RSJ, Friston KJ, Fritch CD, Dolan RJ, Price CJ, Penny WD (eds) Human brain function, 2nd edn. Academic Press, New York, pp 867–880Google Scholar
  58. 58.
    Badillo S, Desmidt S, Ciuciu P (2010) A group level fMRI comparative study between 12 and 32 channel coils at 3 Tesla. In: 16th annual meeting of the organization for human brain mapping (HBM). Barcelona, Spain, p 937Google Scholar
  59. 59.
    Chaari L, Pesquet JC, Tourneret JY, Ciuciu P, Benazza-Benyahia A (2010b) A hierarchical Bayesian model for frame representation. IEEE Trans Signal Process 5560–5571Google Scholar
  60. 60.
    Roche A (2011) A four-dimensional registration algorithm with application to joint correction of motion and slice timing in fMRI. IEEE Trans Med Imaging 30:1546–1554PubMedCrossRefGoogle Scholar
  61. 61.
    Van De Ville D, Seghier M, Lazeyras F, Blu T, Unser M (2007) WSPM: wavelet-based statistical parametric mapping. Neuroimage 37:1205–1217CrossRefGoogle Scholar
  62. 62.
    Moreau JJ (1965) Proximité et dualité dans un espace hilbertien. Bull de la Société Math de Fr 93:273–299Google Scholar
  63. 63.
    Chaux C, Combettes P, Pesquet JC, Wajs VR (2007) A variational formulation for frame-based inverse problems. Inverse Probl 23:1495–1518CrossRefGoogle Scholar
  64. 64.
    Combettes PL, Wajs VR (2005) Signal recovery by proximal forward–backward splitting. Multiscale Model Simul 4:1168–1200CrossRefGoogle Scholar
  65. 65.
    Combettes PL, Pesquet JC (2010) Proximal splitting methods in signal processing. In: Bauschke HH, Burachik R, Combettes PL, Elser V, Luke DR, Wolkowicz H (eds) Fixed-point algorithms for inverse problems in science and engineering, chap 1. Springer, New York, pp 185–212Google Scholar
  66. 66.
    Combettes PL, Pesquet JC (2007) A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery. IEEE J Sel Top Signal Process 1:564–574CrossRefGoogle Scholar

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

Personalised recommendations