Performance Evaluation of CS-MRI Reconstruction Algorithms

  • Bhabesh DekaEmail author
  • Sumit Datta
Part of the Springer Series on Bio- and Neurosystems book series (SSBN, volume 9)


Performances of various compressed sensing reconstruction algorithms are compared under a common simulation environment with different real and synthetic MRI datasets. From experimental results, it has been observed that composite splitting based algorithms outperform others in terms of reconstruction quality, CPU time, and visual results. Additionally, to demonstrate the effectiveness of iterative reweighting an adaptive weighting scheme is combined with a fast composite splitting algorithm and its improvements are also presented.


  1. 1.
    Afonso, M., Bioucas-Dias, J., Figueiredo, M.: Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Process. 19(9), 2345–2356 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bioucas-Dias, J.M., Figueiredo, M.A.T.: A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans. Image Process. 16(12), 2992–3004 (2007)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Candes, E., Tao, T.: Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Candes, E., Wakin, M., Boyd, S.: Enhancing sparsity by reweighted L1 minimization. J. Fourier Anal. Appl. 14(5), 877–905 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Datta, S., Deka, B.: Efficient adaptive weighted minimization for compressed sensing magnetic resonance image reconstruction. In: Proceedings of the Tenth Indian Conference on Computer Vision, Graphics and Image Processing, ICVGIP 16, pp. 95:1–95:8. ACM, New York (2016)Google Scholar
  7. 7.
    Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Daubechies, I., Devore, R., Fornasier, M., Gunturk, C.: Iteratively reweighted least squares minimization for sparse recovery. Commun. Pure Appl. Math. 63(1), 1–38 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Deka, B., Datta, S.: Weighted wavelet tree sparsity regularization for compressed sensing magnetic resonance image reconstruction. In: Advances in Electronics, Communication and Computing, Lecture Notes in Electrical Engineering, vol. 443, pp. 449–457. Springer, Singapore (2017)Google Scholar
  10. 10.
    Figueiredo, M., Nowak, R., Wright, S.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2008)CrossRefGoogle Scholar
  11. 11.
    Gorodnitsky, I.F., Rao, B.D.: Sparse signal reconstruction from limited data using FOCUSS: a reweighted minimum norm algorithm. IEEE Trans. Signal Process. 45(3), 600–616 (1997)CrossRefGoogle Scholar
  12. 12.
    Holland, P.W., Welsch, R.E.: Robust regression using iteratively reweighted least-squares. Commun. Stat. Theory Methods 6(9), 813–827 (1977)CrossRefGoogle Scholar
  13. 13.
    Huang, J., Zhang, S., Li, H., Metaxas, D.N.: Composite splitting algorithms for convex optimization. Comput. Vis. Image Underst. 115(12), 1610–1622 (2011)CrossRefGoogle Scholar
  14. 14.
    Huang, J., Zhang, S., Metaxas, D.N.: Efficient MR image reconstruction for compressed MR imaging. Med. Image Anal. 15(5), 670–679 (2011)CrossRefGoogle Scholar
  15. 15.
    Kim, S., Koh, K., Lustig, M., Boyd, S., Gorinevsky, D.: An interior-point method for largescale \(L_1\)-regularized least squares. IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2008)Google Scholar
  16. 16.
    Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58, 1182–1195 (2007)CrossRefGoogle Scholar
  17. 17.
    Ma, S., Yin, W., Zhang, Y., Chakraborty, A.: An efficient algorithm for compressed MR imaging using total variation and wavelets. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2008), pp. 1–8. Anchorage, AK (2008)Google Scholar
  18. 18.
    Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)CrossRefGoogle Scholar
  19. 19.
    Wright, S.J., Nowak, R.D., Figueiredo, M.A.T.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 2479–2493 (2009)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Yang, J., Zhang, Y., Yin, W.: A fast alternating direction method for TV\(L_1\)-\(L_2\) signal reconstruction from partial Fourier data. IEEE J. Sel. Top. Signal Process. 4(2), 288–297 (2010)CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Electronics and Communication EngineeringTezpur UniversityTezpurIndia

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