Efficient Preconditioning in Joint Total Variation Regularized Parallel MRI Reconstruction

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9350)


Parallel magnetic resonance imaging (pMRI) is a useful technique to aid clinical diagnosis. In this paper, we develop an accelerated algorithm for joint total variation (JTV) regularized calibrationless Parallel MR image reconstruction. The algorithm minimizes a linear combination of least squares data fitting term and the joint total variation regularization. This model has been demonstrated as a very powerful tool for parallel MRI reconstruction. The proposed algorithm is based on the iteratively reweighted least squares (IRLS) framework, which converges exponentially fast. It is further accelerated by preconditioned conjugate gradient method with a well-designed preconditioner. Numerous experiments demonstrate the superior performance of the proposed algorithm for parallel MRI reconstruction in terms of both accuracy and efficiency.


Preconditioned Conjugate Gradient Preconditioned Conjugate Gradient Method Iteratively Reweighted Little Square Linear Convergence Rate Preconditioned Conjugate Gradient Iteration 
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  1. 1.
    Chen, C., Huang, J., He, L., Li, H.: Preconditioning for accelerated iteratively reweighted least squares in structured sparsity reconstruction. In: CVPR 2014, pp. 2713–2720. IEEE (2014)Google Scholar
  2. 2.
    Chen, C., Li, Y., Huang, J.: Calibrationless parallel MRI with joint total variation regularization. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013, Part III. LNCS, vol. 8151, pp. 106–114. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Daubechies, I., DeVore, R., Fornasier, M., Güntürk, C.S.: Iteratively reweighted least squares minimization for sparse recovery. Comm. on Pure and Applied Math. 63(1), 1–38 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Griswold, M.A., Jakob, P.M., Heidemann, R.M., Nittka, M., Jellus, V., Wang, J., Kiefer, B., Haase, A.: Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn. Reson. Med. 47(6), 1202–1210 (2002)CrossRefGoogle Scholar
  5. 5.
    Huang, J., Zhang, S., Li, H., Metaxas, D.: Composite splitting algorithms for convex optimization. Computer Vision and Image Understanding 115(12), 1610–1622 (2011)CrossRefGoogle Scholar
  6. 6.
    Huang, J., Zhang, S., Metaxas, D.: Efficient MR image reconstruction for compressed MR imaging. Medical Image Analysis 15(5), 670–679 (2011)CrossRefGoogle Scholar
  7. 7.
    Hunter, D.R., Lange, K.: A tutorial on MM algorithms. The Amer. Stat. 58(1), 30–37 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Liang, D., Liu, B., Wang, J., Ying, L.: Accelerating SENSE using compressed sensing. Magn. Reson. Med. 62(6), 1574–1584 (2009)CrossRefGoogle Scholar
  9. 9.
    Lustig, M., Pauly, J.M.: SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space. Magn. Reson. Med. 64(2), 457–471 (2010)Google Scholar
  10. 10.
    Majumdar, A., Ward, R.K.: Calibration-less multi-coil mr image reconstruction. Magn. Reson. Imag. 30(7), 1032–1045 (2012)CrossRefGoogle Scholar
  11. 11.
    Pruessmann, K.P., Weiger, M., Scheidegger, M.B., Boesiger, P., et al.: SENSE: sensitivity encoding for fast MRI. Magn. Reson. Med. 42(5), 952–962 (1999)CrossRefGoogle Scholar
  12. 12.
    Saad, Y.: Iterative methods for sparse linear systems. Siam (2003)Google Scholar
  13. 13.
    Sawyer, A.M., Lustig, M., Alley, M., Uecker, P., Virtue, P., Lai, P., Vasanawala, S., Healthcare, G.: Creation of fully sampled MR data repository for compressed sensing of the knee (2013)Google Scholar
  14. 14.
    Shewchuk, J.R.: An introduction to the conjugate gradient method without the agonizing pain (1994)Google Scholar
  15. 15.
    Shin, P.J., Larson, P.E., Ohliger, M.A., Elad, M., Pauly, J.M., Vigneron, D.B., Lustig, M.: Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion. Magn. Reson. Med. 72(4), 959–970 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity of Texas at ArlingtonArlingtonUSA
  2. 2.Department of RadiologyNew York UniversityNew YorkUSA

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