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Multi-tasking to Correct: Motion-Compensated MRI via Joint Reconstruction and Registration

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Scale Space and Variational Methods in Computer Vision (SSVM 2019)


This work addresses a central topic in Magnetic Resonance Imaging (MRI) which is the motion-correction problem in a joint reconstruction and registration framework. From a set of multiple MR acquisitions corrupted by motion, we aim at - jointly - reconstructing a single motion-free corrected image and retrieving the physiological dynamics through the deformation maps. To this purpose, we propose a novel variational model. First, we introduce an \(L^2\) fidelity term, which intertwines reconstruction and registration along with the weighted total variation. Second, we introduce an additional regulariser which is based on the hyperelasticity principles to allow large and smooth deformations. We demonstrate through numerical results that this combination creates synergies in our complex variational approach resulting in higher quality reconstructions and a good estimate of the breathing dynamics. We also show that our joint model outperforms in terms of contrast, detail and blurring artefacts, a sequential approach.

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  1. 1.

  2. 2.


  1. Adluru, G., DiBella, E.V., Schabel, M.C.: Model-based registration for dynamic cardiac perfusion MRI. J. Magn. Reson. Imaging 24(5), 1062–70 (2006)

    Article  Google Scholar 

  2. Aviles-Rivero, A.I., Williams, G., Graves, M.J., Schönlieb, C.B.: Compressed sensing plus motion (CS+M): a new perspective for improving undersampled MR image reconstruction. arXiv preprint arXiv:1810.10828 (2018)

  3. Baldi, A.: Weighted BV functions. Houston J. Math. 27(3), 683–705 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Ball, J.M.: Global invertibility of Sobolev functions and the interpenetration of matter. Proc. Roy. Soc. Edinb. A 88(3–4), 315–328 (1981)

    Article  MathSciNet  Google Scholar 

  5. Baumgartner, C.F., Kolbitsch, C., McClelland, J.R., Rueckert, D., King, A.P.: Autoadaptive motion modelling for MR-based respiratory motion estimation. Med. Image Anal. 35, 83–100 (2017)

    Article  Google Scholar 

  6. Blume, M., Martinez-Moller, A., Keil, A., Navab, N., Rafecas, M.: Joint reconstruction of image and motion in gated positron emission tomography. IEEE Trans. Med. Imaging 29(11), 1892–1906 (2010)

    Article  Google Scholar 

  7. Bresson, X., Esedo\(\bar{\rm g}\)lu, S., Vandergheynst, P., Thiran, J.P., Osher, S.: Fast global minimization of the active contour/snake model. J. Math. Imaging Vis. 28(2), 151–167 (2007)

    Article  MathSciNet  Google Scholar 

  8. Burger, M., Dirks, H., Schönlieb, C.B.: A variational model for joint motion estimation and image reconstruction. SIAM J. Imaging Sci. 11(1), 94–128 (2018)

    Article  MathSciNet  Google Scholar 

  9. Burger, M., Modersitzki, J., Ruthotto, L.: A hyperelastic regularization energy for image registration. SIAM J. Sci. Comput. 35(1), B132–B148 (2013)

    Article  MathSciNet  Google Scholar 

  10. Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20(1), 89–97 (2004)

    MathSciNet  MATH  Google Scholar 

  11. Chun, S., Fessler, J.: Joint image reconstruction and nonrigid motion estimation with a simple penalty that encourages local invertibility. In: Proceedings of the SPIE, vol. 7258

    Google Scholar 

  12. Demengel, F., Demengel, G., Erné, R.: Functional Spaces for the Theory of Elliptic Partial Differential Equations. Universitext. Springer, London (2012).

    Book  MATH  Google Scholar 

  13. Droske, M., Rumpf, M.: A variational approach to nonrigid morphological image registration. SIAM J. Appl. Math. 64(2), 668–687 (2004)

    Article  MathSciNet  Google Scholar 

  14. Gupta, S.N., Solaiyappan, M., Beache, G.M., Arai, A.E., Foo, T.K.: Fast method for correcting image misregistration due to organ motion in time-series MRI data. Magn. Reson. Med. 49(3), 506–514 (2003)

    Article  Google Scholar 

  15. Jansen, M., Kuijf, H., Veldhuis, W., Wessels, F., Van Leeuwen, M., Pluim, J.: Evaluation of motion correction for clinical dynamic contrast enhanced MRI of the liver. Phys. Med. Biol. 62(19), 7556 (2017)

    Article  Google Scholar 

  16. Johansson, A., Balter, J., Cao, Y.: Rigid-body motion correction of the liver in image reconstruction for golden-angle stack-of-stars DCE MRI. Magn. Reson. Med. 79(3), 1345–1353 (2018)

    Article  Google Scholar 

  17. Ledesma-Carbayo, M.J., Kellman, P., Arai, A.E., McVeigh, E.R.: Motion corrected free-breathing delayed-enhancement imaging of myocardial infarction using nonrigid registration. J. Magn. Reson. Imaging 26(1), 184–90 (2007)

    Article  Google Scholar 

  18. 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)

    Article  Google Scholar 

  19. Mair, B.A., Gilland, D.R., Sun, J.: Estimation of images and nonrigid deformations in gated emission CT. IEEE Trans. Med. Imaging 25(9), 1130–1144 (2006)

    Article  Google Scholar 

  20. Modersitzki, J.: FAIR: Flexible Algorithms for Image Registration. SIAM, Philadelphia (2009)

    Book  Google Scholar 

  21. Odille, F., et al.: Joint reconstruction of multiple images and motion in MRI: application to free-breathing myocardial T2 quantification. IEEE Trans. Med. Imaging 35(1), 197–207 (2016)

    Article  Google Scholar 

  22. Schumacher, H., Modersitzki, J., Fischer, B.: Combined reconstruction and motion correction in SPECT imaging. ITNS 56(1), 73–80 (2009)

    Google Scholar 

  23. von Siebenthal, M., Szekely, G., Gamper, U., Boesiger, P., Lomax, A., Cattin, P.: 4D MR imaging of respiratory organ motion and its variability. Phys. Med. Biol. 52(6), 1547 (2007)

    Article  Google Scholar 

  24. Tomasi, C., Kanade, T.: Shape and motion from image streams under orthography: a factorization method. Int. J. Comput. Vis. 9, 137–154 (1992)

    Article  Google Scholar 

  25. de Vos, B.D., Berendsen, F.F., Viergever, M.A., Staring, M., Išgum, I.: End-to-end unsupervised deformable image registration with a convolutional neural network. In: Cardoso, M.J., et al. (eds.) DLMIA/ML-CDS -2017. LNCS, vol. 10553, pp. 204–212. Springer, Cham (2017).

    Chapter  Google Scholar 

  26. Yang, X., Kwitt, R., Styner, M., Niethammer, M.: Quicksilver: fast predictive image registration-a deep learning approach. NeuroImage 158, 378–396 (2017)

    Article  Google Scholar 

  27. Zaitsev, M., Maclaren, J., Herbst, M.: Motion artifacts in MRI: a complex problem with many partial solutions. J. Magn. Reson. Imaging 42(4), 887–901 (2015)

    Article  Google Scholar 

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VC acknowledges the financial support of the Cambridge Cancer Centre. Support from the CMIH and CCIMI University of Cambridge is greatly acknowledged.

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Correspondence to Veronica Corona .

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Corona, V. et al. (2019). Multi-tasking to Correct: Motion-Compensated MRI via Joint Reconstruction and Registration. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham.

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