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Accelerated Dynamic MRI Using Kernel-Based Low Rank Constraint

  • Image & Signal Processing
  • Published:
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Abstract

We present a novel reconstruction method for dynamic MR images from highly under-sampled k-space measurements. The reconstruction problem is posed as spectrally regularized matrix recovery problem, where kernel-based low rank constraint is employed to effectively utilize the non-linear correlations between the images in the dynamic sequence. Unlike other kernel-based methods, we use a single-step regularized reconstruction approach to simultaneously learn the kernel basis functions and the weights. The objective function is optimized using variable splitting and alternating direction method of multipliers. The framework can seamlessly handle additional sparsity constraints such as spatio-temporal total variation. The algorithm performance is evaluated on a numerical phantom and in vivo data sets and it shows significant improvement over the comparison methods.

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References

  1. Afonso, M. V., Bioucas-Dias, J. M., and Figueiredo, M. A., Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Process. 19(9):2345–2356, 2010.

    Article  PubMed  Google Scholar 

  2. Arias, P., Randall, G., and Sapiro, G.: Connecting the out-of-sample and pre-image problems in kernel methods. In: IEEE Conference on Computer Vision and Pattern Recognition, 2007. CVPR’07, pp. 1–8. IEEE, 2007.

  3. Arif, O., Vela, P., and Daley, W.: Pre-image problem in manifold learning and dimensional reduction methods. In: 2010 Ninth International Conference on Machine Learning and Applications, pp. 921–924. IEEE, 2010.

  4. Belkin, M., and Niyogi, P., Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6):1373–1396, 2003.

    Article  Google Scholar 

  5. Bengio, Y., Paiement, J., Vincent, P., Delalleau, O., Roux, N. L., and Ouimet, M.: Out-of-sample extensions for LLE, isomap, MDS, eigenmaps, and spectral clustering. In: Advances in Neural Information Processing Systems, p. 177, 2004.

  6. Boyd, S., Parikh, N., Chu, E., Peleato, B., and Eckstein, J., Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends®;, in Machine Learning 3(1): 1–122, 2011.

    Article  Google Scholar 

  7. Buerger, C., Clough, R. E., King, A. P., Schaeffter, T., and Prieto, C., Nonrigid motion modeling of the liver from 3-d undersampled self-gated golden-radial phase encoded MRI. IEEE Trans. Med. Imaging 31(3): 805–815, 2012.

    Article  CAS  PubMed  Google Scholar 

  8. Chen, X., Usman, M., Baumgartner, C. F., Balfour, D. R., Marsden, P. K., Reader, A. J., Prieto, C., and King, A. P., High-resolution self-gated dynamic abdominal MRI using manifold alignment. IEEE Trans. Med. Imaging 36(4):960–971, 2017.

    Article  PubMed  Google Scholar 

  9. Donoho, D. L., Compressed sensing. IEEE Trans. Inf. Theory 52(4):1289–1306, 2006.

    Article  Google Scholar 

  10. Eckstein, J., and Bertsekas, D. P., On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55(1):293–318 , 1992.

    Article  Google Scholar 

  11. Elad, M., Milanfar, P., and Rubinstein, R., Analysis versus synthesis in signal priors. Inverse Prob. 23 (3):947, 2007.

    Article  Google Scholar 

  12. Feng, L., Grimm, R., Block, K. T., Chandarana, H., Kim, S., Xu, J., Axel, L., Sodickson, D. K., and Otazo, R., Golden-angle radial sparse parallel MRI: Combination of compressed sensing, parallel imaging, and golden-angle radial sampling for fast and flexible dynamic volumetric MRI. Magn. Reson. Med. 72(3):707–717, 2014.

    Article  PubMed  Google Scholar 

  13. Feng, L., Axel, L., Chandarana, H., Block, K. T., Sodickson, D. K., and Otazo, R., Xd-grasp: Golden-angle radial MRI with reconstruction of extra motion-state dimensions using compressed sensing. Magn. Reson. Med. 75(2):775–788, 2016.

    Article  PubMed  Google Scholar 

  14. Glover, G. H., and Pauly, J. M., Projection reconstruction techniques for reduction of motion effects in MRI. Magn. Reson. Med. 28(2):275–289, 1992.

    Article  CAS  PubMed  Google Scholar 

  15. Haldar, J. P., and Liang, Z. P.: Spatiotemporal imaging with partially separable functions: a matrix recovery approach. In: 2010 IEEE International Symposium on Biomedical imaging: from Nano to Macro, pp. 716–719. IEEE, 2010.

  16. King, A. P., Buerger, C., Tsoumpas, C., Marsden, P. K., and Schaeffter, T., Thoracic respiratory motion estimation from MRI using a statistical model and a 2-d image navigator. Med. Image Anal. 16(1):252–264, 2012.

    Article  CAS  PubMed  Google Scholar 

  17. Larkman, D. J., and Nunes, R. G., Parallel magnetic resonance imaging. Phys. Med. Biol. 52(7):R15, 2007.

    Article  PubMed  Google Scholar 

  18. Larson, A. C., White, R. D., Laub, G., McVeigh, E. R., Li, D., and Simonetti, O. P., Self-gated cardiac cine MRI. Magn. Reson. Med. 51(1):93–102, 2004.

    Article  PubMed  PubMed Central  Google Scholar 

  19. Li, X., Arlinghaus, L. R., Ayers, G. D., Chakravarthy, A. B., Abramson, R. G., Abramson, V. G., Atuegwu, N., Farley, J., Mayer, I. A., Kelley, M. C., et al., Dce-MRI analysis methods for predicting the response of breast cancer to neoadjuvant chemotherapy: Pilot study findings. Magn. Reson. Med. 71 (4):1592–1602, 2014.

    Article  PubMed  Google Scholar 

  20. Liang, Z. P.: Spatiotemporal imagingwith partially separable functions. In: 4th IEEE International Symposium on Biomedical Imaging: from Nano to Macro, 2007. ISBI 2007, pp. 988–991. IEEE, 2007.

  21. Lin, W., Guo, J., Rosen, M. A., and Song, H. K., Respiratory motion-compensated radial dynamic contrast-enhanced (DCE)-MRI of chest and abdominal lesions. Magn. Reson. Med. 60(5):1135–1146, 2008.

    Article  PubMed  PubMed Central  Google Scholar 

  22. Lingala, S. G., Hu, Y., DiBella, E., and Jacob, M., Accelerated dynamic MRI exploiting sparsity and low-rank structure: kt slr. IEEE Trans. Med. Imaging 30(5):1042–1054, 2011.

    Article  PubMed  PubMed Central  Google Scholar 

  23. Liu, J., Spincemaille, P., Codella, N. C., Nguyen, T. D., Prince, M. R., and Wang, Y., Respiratory and cardiac self-gated free-breathing cardiac cine imaging with multiecho 3d hybrid radial ssfp acquisition. Magn. Reson. Med. 63(5):1230–1237, 2010.

    Article  PubMed  PubMed Central  Google Scholar 

  24. Lustig, M., Santos, J. M., Donoho, D. L., and Pauly, J. M.: kt sparse: High frame rate dynamic MRI exploiting spatio-temporal sparsity. In: Proceedings of the 13th Annual Meeting of ISMRM. Vol. 2420. Seattle, 2006

  25. Lustig, M., Donoho, D., and Pauly, J. M., Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58(6):1182–1195, 2007.

    Article  PubMed  Google Scholar 

  26. Majumdar, A., and Ward, R. K., An algorithm for sparse MRI reconstruction by schatten p-norm minimization. Magn. Reson. Imaging 29(3):408–417, 2011.

    Article  PubMed  Google Scholar 

  27. Nakarmi, U., Wang, Y., Lyu, J., and Ying, L.: Dynamic magnetic resonance imaging using compressed sensing with self-learned nonlinear dictionary (nl-d). In: 2015 IEEE 12Th International Symposium on Biomedical Imaging (ISBI), pp. 331–334. IEEE, 2015.

  28. Nakarmi, U., Zhou, Y., Lyu, J., Slavakis, K., and Ying, L.: Accelerating dynamic magnetic resonance imaging by nonlinear sparse coding. In: 2016 IEEE 13Th International Symposium on Biomedical Imaging (ISBI), pp. 510–513. IEEE, 2016.

  29. Nakarmi, U., Wang, Y., Lyu, J., Liang, D., and Ying, L., A kernel-based low-rank (klr) model for low-dimensional manifold recovery in highly accelerated dynamic MRI. IEEE Trans. Med. Imaging 36(11):2297–2307, 2017.

    Article  PubMed  PubMed Central  Google Scholar 

  30. Nawaz, M. Z., and Arif, O.: Robust kernel embedding of conditional and posterior distributions with applications. In: 2016 15Th IEEE International Conference on Machine Learning and Applications (ICMLA), pp. 39–44. IEEE, 2016.

  31. Nocedal, J., and Wright, S. J., Sequential Quadratic Programming. Berlin: Springer, 2006.

    Google Scholar 

  32. Otazo, R., Kim, D., Axel, L., and Sodickson, D. K., Combination of compressed sensing and parallel imaging for highly accelerated first-pass cardiac perfusion MRI. Magn. Reson. Med. 64(3):767–776, 2010.

    Article  PubMed  PubMed Central  Google Scholar 

  33. Pedersen, H., Kozerke, S., Ringgaard, S., Nehrke, K., and Kim, W. Y., k-t pca: Temporally constrained k-t blast reconstruction using principal component analysis. Magn. Reson. Med. 62(3):706–716, 2009.

    Article  PubMed  Google Scholar 

  34. Peters, D. C., Lederman, R. J., Dick, A. J., Raman, V. K., Guttman, M. A., Derbyshire, J. A., and McVeigh, E. R., Undersampled projection reconstruction for active catheter imaging with adaptable temporal resolution and catheter-only views. Magn. Reson. Med. 49(2):216–222, 2003.

    Article  PubMed  PubMed Central  Google Scholar 

  35. Poddar, S., and Jacob, M., Dynamic MRI using smoothness regularization on manifolds (storm). IEEE Trans. Med. Imaging 35(4):1106–1115, 2016.

    Article  PubMed  Google Scholar 

  36. Ramani, S., and Fessler, J. A., Parallel MR image reconstruction using augmented lagrangian methods. IEEE Trans. Med. Imaging 30(3):694–706, 2011.

    Article  PubMed  Google Scholar 

  37. Roweis, S. T., and Saul, L. K., Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326, 2000.

    Article  CAS  PubMed  Google Scholar 

  38. Santelli, C., Nezafat, R., Goddu, B., Manning, W. J., Smink, J., Kozerke, S., and Peters, D. C., Respiratory bellows revisited for motion compensation: Preliminary experience for cardiovascular MR. Magn. Reson. Med. 65(4):1097–1102, 2011.

    Article  PubMed  Google Scholar 

  39. Schölkopf, B., Smola, A., and Müller, K. R., Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10(5):1299–1319, 1998.

    Article  Google Scholar 

  40. Scholköpf, B., Smola, A., and Muller, K. R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 1299–1319, 1998

    Article  Google Scholar 

  41. Sharif, B., and Bresler, Y.: Physiologically improved ncat phantom (pincat) enables in-silico study of the effects of beat-to-beat variability on cardiac MR. In: Proceedings of the Annual Meeting of ISMRM. Vol. 3418. Berlin, 2007

  42. Trémoulhéac, B, Dikaios, N., Atkinson, D., and Arridge, S. R., Dynamic MR image reconstruction–separation from undersampled k-space via low-rank plus sparse prior. IEEE Trans. Med. Imaging 33 (8):1689–1701, 2014.

    Article  PubMed  Google Scholar 

  43. Tsao, J., Boesiger, P., and Pruessmann, K. P., k-t blast and k-t sense: Dynamic MRI with high frame rate exploiting spatiotemporal correlations. Magn. Reson. Med. 50(5):1031–1042, 2003.

    Article  PubMed  Google Scholar 

  44. Usman, M., Vaillant, G., Atkinson, D., Schaeffter, T., and Prieto, C., Compressive manifold learning: Estimating one-dimensional respiratory motion directly from undersampled k-space data. Magn. Reson. Med. 72(4): 1130–1140, 2014.

    Article  PubMed  Google Scholar 

  45. Wang, V. J., and Castanon, D.: Kernel low rank representation. Boston University-Center for Information & Systems Engineering, Tech Rep, 2011

  46. Wang, Y., and Ying, L.: Undersampled dynamic magnetic resonance imaging using kernel principal component analysis. In: 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 1533–1536. IEEE, 2014.

  47. Wang, Y., Yang, J., Yin, W., and Zhang, Y., A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. 1(3):248–272, 2008.

    Article  Google Scholar 

  48. Winkelmann, S., Schaeffter, T., Koehler, T., Eggers, H., and Doessel, O., An optimal radial profile order based on the golden ratio for time-resolved MRI. IEEE Trans. Med. Imaging 26(1):68–76, 2007.

    Article  PubMed  Google Scholar 

  49. Abdullah, S., Arif, O., Arif, M.B., and Mahmood, T.: MRI Reconstruction from sparse K-space data using low dimensional manifold model. IEEE Access, https://doi.org/10.1109/ACCESS.2019.2925051, 2019

    Article  Google Scholar 

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Authors and Affiliations

  1. National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Omar Arif, Hammad Afzal, Haider Abbas & Muhammad Faisal Amjad

  2. South China University of Technology, Guangzhou, China

    Jiafu Wan

  3. Manchester Metropolitan University, Manchester, UK

    Raheel Nawaz

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  1. Omar Arif
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  2. Hammad Afzal
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  4. Muhammad Faisal Amjad
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  6. Raheel Nawaz
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Correspondence to Omar Arif.

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Arif, O., Afzal, H., Abbas, H. et al. Accelerated Dynamic MRI Using Kernel-Based Low Rank Constraint. J Med Syst 43, 271 (2019). https://doi.org/10.1007/s10916-019-1399-x

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