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Directional tensor product complex tight framelets for compressed sensing MRI reconstruction

Directional tensor product complex tight framelets for compressed sensing MRI reconstruction

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Compressed sensing magnetic resonance imaging (CS-MRI) is an effective way of reducing the sampling data in the k-space and shortening the scanning time. Motivated by the high performance of directional tensor product complex tight framelets (TPCTFs) for the image denoising problem, the authors proposed a novel framework that integrated TPCTF for sparse representation and projected fast iterative soft-thresholding algorithm (pFISTA) for CS-MRI reconstruction. Furthermore, to take advantage of the cross-scale relations in the wavelet tree of frame coefficients, the bivariate shrinkage (BS) function with local variance estimation is proposed to shrink thresholding. Such TPCTFs can provide sparse directional representations very well for MR image. When compared with other the state-of-the-art CS-MRI algorithms in numerical experiments, the proposed TPCTF-BS method achieves a higher reconstruction quality with respect to image edge preservation and the artefact suppression.

References

    1. 1)
      • 1. Lustig, M., Donoho, D.L., Santos, J.M., et al: ‘Compressed sensing MRI’, IEEE Signal Process. Mag., 2008, 25, (2), pp. 7282.
    2. 2)
      • 2. Donoho, D.L.: ‘Compressed sensing’, IEEE Trans. Inf. Theory, 2006, 52, (4), pp. 12891306.
    3. 3)
      • 3. Shi, B., Lian, Q., Chen, S.: ‘Compressed sensing magnetic resonance imaging based on dictionary updating and block-matching and three-dimensional filtering regularisation’, IET Image Process., 2016, 10, (1), pp. 6879.
    4. 4)
      • 4. Wang, S., Tan, S., Gao, Y., et al: ‘Learning joint-sparse codes for calibration-free parallel MR imaging’, IEEE Trans. Med. Imaging, 2018, 37, (1), pp. 251261.
    5. 5)
      • 5. Wang, S., Liu, J., Liu, Q., et al: ‘Iterative feature refinement for accurate undersampled MR image reconstruction’, Phys. Med. Biol., 2016, 61, (9), p. 3291.
    6. 6)
      • 6. Wang, S., Liu, J., Peng, X., et al: ‘Two-layer tight frame sparsifying model for compressed sensing magnetic resonance imaging’, BioMed Res. Int., 2016, 2016, pp. 17.
    7. 7)
      • 7. Elad, M., Milanfar, P., Rubinstein, R.: ‘Analysis versus synthesis in signal priors’, Inverse Probl., 2007, 23, (3), p. 947.
    8. 8)
      • 8. Do, M.N., Vetterli, M.: ‘The contourlet transform: an efficient directional multiresolution image representation’, IEEE Trans. Image Process., 2005, 14, (12), pp. 20912106.
    9. 9)
      • 9. Li, C., Yin, W., Zhang, Y.: ‘User's guide for Tval3: TV Minimization by augmented Lagrangian and alternating direction algorithms’, CAAM report, 2009, 20, pp. 4647.
    10. 10)
      • 10. Wang, Y., Yang, J., Yin, W., et al: ‘A new alternating minimization algorithm for total variation image reconstruction’, SIAM J. Imaging Sci., 2008, 1, (3), pp. 248272.
    11. 11)
      • 11. Qu, X., Guo, D., Ning, B., et al: ‘Undersampled MRI reconstruction with patch-based directional wavelets’, Magn. Reson. Imaging, 2012, 30, (7), pp. 964977.
    12. 12)
      • 12. Ning, B., Qu, X., Guo, D., et al: ‘Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization’, Magn. Reson. Imaging, 2013, 31, (9), pp. 16111622.
    13. 13)
      • 13. Ravishankar, S., Bresler, Y.: ‘Mr image reconstruction from highly undersampled K-space data by dictionary learning’, IEEE Trans. Med. Imaging, 2011, 30, (5), pp. 10281041.
    14. 14)
      • 14. Zhan, Z., Cai, J.-F., Guo, D., et al: ‘Fast multiclass dictionaries learning with geometrical directions in MRI reconstruction’, IEEE Trans. Biomed. Eng., 2016, 63, (9), pp. 18501861.
    15. 15)
      • 15. Zhang, J., Zhao, D., Gao, W.: ‘Group-based sparse representation for image restoration’, IEEE Trans. Image Process., 2014, 23, (8), pp. 33363351.
    16. 16)
      • 16. Cai, J.-F., Chan, R.H., Shen, Z.: ‘A framelet-based image inpainting algorithm’, Appl. Comput. Harmon. Anal., 2008, 24, (2), pp. 131149.
    17. 17)
      • 17. Liu, Y., Cai, J.-F., Zhan, Z., et al: ‘Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging’, PLOS One, 2015, 10, (4), p. e0119584.
    18. 18)
      • 18. Selesnick, I.W., Baraniuk, R.G., Kingsbury, N.C.: ‘The dual-tree complex wavelet transform’, IEEE Signal Process. Mag., 2005, 22, (6), pp. 123151.
    19. 19)
      • 19. Han, B., Zhao, Z.: ‘Tensor product complex tight framelets with increasing directionality’, SIAM J. Imaging Sci., 2014, 7, (2), pp. 9971034.
    20. 20)
      • 20. Shen, Y., Han, B., Braverman, E.: ‘Image inpainting using directional tensor product complex tight framelets’, arXiv preprint arXiv:1407.3234, 2014.
    21. 21)
      • 21. Shen, Y., Han, B., Braverman, E.: ‘Removal of mixed Gaussian and impulse noise using directional tensor product Complex tight framelets’, J. Math. Imaging Vis., 2016, 54, (1), pp. 6477.
    22. 22)
      • 22. Liu, Y., Zhan, Z., Cai, J.-F., et al: ‘Projected iterative soft-thresholding algorithm for tight frames in compressed sensing magnetic resonance imaging’, IEEE Trans. Med. Imaging, 2016, 35, (9), pp. 21302140.
    23. 23)
      • 23. Boyd, S., Parikh, N., Chu, E., et al: ‘Distributed optimization and statistical learning via the alternating direction method of multipliers’, Found. Trends Mach. Learn., 2011, 3, (1), pp. 1122.
    24. 24)
      • 24. Duffin, R.J., Schaeffer, A.C.: ‘A class of nonharmonic Fourier series’, Trans. Am. Math. Soc., 1952, 72, (2), pp. 341366.
    25. 25)
      • 25. Han, B.: ‘Properties of discrete framelet transforms’, Math. Model. Nat. Phenom., 2013, 8, (1), pp. 1847.
    26. 26)
      • 26. Shen, Y., Han, B., Braverman, E.: ‘Image inpainting from partial noisy data by directional complex tight framelets’, ANZIAM J., 2017, 58, (3–4), pp. 247255.
    27. 27)
      • 27. Parikh, N., Boyd, S.: ‘Proximal algorithms’, Found. Trends Optim., 2014, 1, (3), pp. 127239.
    28. 28)
      • 28. Beck, A., Teboulle, M.: ‘A fast iterative shrinkage-thresholding algorithm for linear inverse problems’. SIAM J. Imaging Sci., 2009, 2, (1), pp. 183202.
    29. 29)
      • 29. Sendur, L., Selesnick, I.W.: ‘Bivariate shrinkage with local variance estimation’, IEEE Signal Process. Lett., 2002, 9, (12), pp. 438441.
    30. 30)
      • 30. Huang, J., Zhang, S., Metaxas, D.: ‘Efficient MR image reconstruction for compressed Mr imaging’, Med. Image Anal., 2011, 15, (5), pp. 670679.
    31. 31)
      • 31. Wang, Z., Bovik, A.C., Sheikh, H.R., et al: ‘Image quality assessment: from error visibility to structural similarity’, IEEE Trans. Image Process., 2004, 13, (4), pp. 600612.
    32. 32)
      • 32. Qu, X., Hou, Y., Lam, F., et al: ‘Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator’, Med. Image Anal., 2014, 18, (6), pp. 843856.
    33. 33)
      • 33. Lai, Z., Qu, X., Liu, Y., et al: ‘Image reconstruction of compressed sensing MRI using graph-based redundant wavelet transform’, Med. Image Anal., 2016, 27, pp. 93104.
    34. 34)
      • 34. Rockinger, O.: ‘Image sequence fusion using a shift-invariant wavelet transform’, IEEE Proc. Int. Conf. Image Process., 1997, 3, pp. 288291.
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