Joint Total Variation ESTATICS for Robust Multi-parameter Mapping | SpringerLink
Skip to main content

Joint Total Variation ESTATICS for Robust Multi-parameter Mapping

  • Conference paper
  • First Online:
Medical Image Computing and Computer Assisted Intervention – MICCAI 2020 (MICCAI 2020)

Abstract

Quantitative magnetic resonance imaging (qMRI) derives tissue-specific parameters – such as the apparent transverse relaxation rate \(R_2^\star \), the longitudinal relaxation rate \(R_1\) and the magnetisation transfer saturation – that can be compared across sites and scanners and carry important information about the underlying microstructure. The multi-parameter mapping (MPM) protocol takes advantage of multi-echo acquisitions with variable flip angles to extract these parameters in a clinically acceptable scan time. In this context, ESTATICS performs a joint loglinear fit of multiple echo series to extract \(R_2^\star \) and multiple extrapolated intercepts, thereby improving robustness to motion and decreasing the variance of the estimators. In this paper, we extend this model in two ways: (1) by introducing a joint total variation (JTV) prior on the intercepts and decay, and (2) by deriving a nonlinear maximum a posteriori estimate. We evaluated the proposed algorithm by predicting left-out echoes in a rich single-subject dataset. In this validation, we outperformed other state-of-the-art methods and additionally showed that the proposed approach greatly reduces the variance of the estimated maps, without introducing bias.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 11439
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 14299
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Ashburner, J., Brudfors, M., Bronik, K., Balbastre, Y.: An algorithm for learning shape and appearance models without annotations. NeuroImage (2018)

    Google Scholar 

  2. Bach, F.: Optimization with sparsity-inducing penalties. FNT Mach. Learn. 4(1), 1–106 (2011)

    Article  Google Scholar 

  3. Bauer, C.M., Jara, H., Killiany, R.: Whole brain quantitative T2 MRI across multiple scanners with dual echo FSE: applications to AD, MCI, and normal aging. NeuroImage 52(2), 508–514 (2010)

    Article  Google Scholar 

  4. Brudfors, M., Balbastre, Y., Nachev, P., Ashburner, J.: MRI super-resolution using multi-channel total variation. In: 22nd Conference on Medical Image Understanding and Analysis, Southampton, UK (2018)

    Google Scholar 

  5. Chen, C., He, L., Li, H., Huang, J.: Fast iteratively reweighted least squares algorithms for analysis-based sparse reconstruction. Med. Image Anal. 49, 141–152 (2018)

    Article  Google Scholar 

  6. Coupé, P., Manjón, J., Robles, M., Collins, D.: Adaptive multiresolution non-local means filter for three-dimensional magnetic resonance image denoising. IET Image Process. 6(5), 558–568 (2012)

    Article  MathSciNet  Google Scholar 

  7. Coupe, P., Yger, P., Prima, S., Hellier, P., Kervrann, C., Barillot, C.: An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images. IEEE Trans. Med. Imaging 27(4), 425–441 (2008)

    Article  Google Scholar 

  8. Daubechies, I., DeVore, R., Fornasier, M., Güntürk, C.S.: Iteratively reweighted least squares minimization for sparse recovery. Commun. Pure Appl. Math. 63(1), 1–38 (2010)

    Article  MathSciNet  Google Scholar 

  9. Deoni, S.C.L., Williams, S.C.R., Jezzard, P., Suckling, J., Murphy, D.G.M., Jones, D.K.: Standardized structural magnetic resonance imaging in multicentre studies using quantitative T1 and T2 imaging at 1.5 T. NeuroImage 40(2), 662–671 (2008)

    Article  Google Scholar 

  10. Dick, F., Tierney, A.T., Lutti, A., Josephs, O., Sereno, M.I., Weiskopf, N.: In vivo functional and myeloarchitectonic mapping of human primary auditory areas. J. Neurosci. 32(46), 16095–16105 (2012)

    Article  Google Scholar 

  11. Donoho, D.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995)

    Article  MathSciNet  Google Scholar 

  12. Hasan, K.M., Walimuni, I.S., Kramer, L.A., Narayana, P.A.: Human brain iron mapping using atlas-based T2 relaxometry. Magn. Reson. Med. 67(3), 731–739 (2012)

    Article  Google Scholar 

  13. Helms, G., Dathe, H., Dechent, P.: Quantitative FLASH MRI at 3T using a rational approximation of the Ernst equation. Magn. Reson. Med. 59(3), 667–672 (2008)

    Article  Google Scholar 

  14. Helms, G., Dathe, H., Kallenberg, K., Dechent, P.: High-resolution maps of magnetization transfer with inherent correction for RF inhomogeneity and T1 relaxation obtained from 3D FLASH MRI. Magn. Reson. Med. 60(6), 1396–1407 (2008)

    Article  Google Scholar 

  15. Huang, J., Chen, C., Axel, L.: Fast multi-contrast MRI reconstruction. In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds.) MICCAI 2012. LNCS, vol. 7510, pp. 281–288. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33415-3_35

    Chapter  Google Scholar 

  16. Lebrun, M., Buades, A., Morel, J.M.: A nonlocal Bayesian image denoising algorithm. SIAM J. Imaging Sci. 6(3), 1665–1688 (2013)

    Article  MathSciNet  Google Scholar 

  17. Liu, T., et al.: Morphology enabled dipole inversion (MEDI) from a single-angle acquisition: comparison with COSMOS in human brain imaging. Magn. Reson. Med. 66(3), 777–783 (2011)

    Article  Google Scholar 

  18. Lutti, A., Hutton, C., Finsterbusch, J., Helms, G., Weiskopf, N.: Optimization and validation of methods for mapping of the radiofrequency transmit field at 3T. Magn. Reson. Med. 64(1), 229–238 (2010)

    Article  Google Scholar 

  19. Manjón, J.V., Coupé, P., Buades, A., Louis Collins, D., Robles, M.: New methods for MRI denoising based on sparseness and self-similarity. Med. Image Anal. 16(1), 18–27 (2012)

    Article  Google Scholar 

  20. Manjón, J.V., Coupé, P., Martí-Bonmatí, L., Collins, D.L., Robles, M.: Adaptive non-local means denoising of MR images with spatially varying noise levels. J. Magn. Reson. Imaging 31(1), 192–203 (2010)

    Article  Google Scholar 

  21. Ogg, R.J., Langston, J.W., Haacke, E.M., Steen, R.G., Taylor, J.S.: The correlation between phase shifts in gradient-echo MR images and regional brain iron concentration. Magn. Reson. Imaging 17(8), 1141–1148 (1999)

    Article  Google Scholar 

  22. Ordidge, R.J., Gorell, J.M., Deniau, J.C., Knight, R.A., Helpern, J.A.: Assessment of relative brain iron concentrations using T2-weighted and T2*-weighted MRI at 3 Tesla. Magn. Reson. Med. 32(3), 335–341 (1994)

    Article  Google Scholar 

  23. Papp, D., Callaghan, M.F., Meyer, H., Buckley, C., Weiskopf, N.: Correction of inter-scan motion artifacts in quantitative R1 mapping by accounting for receive coil sensitivity effects. Magn. Reson. Med. 76(5), 1478–1485 (2016)

    Article  Google Scholar 

  24. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes 3rd Edition: The Art of Scientific Computing, 3rd edn. Cambridge University Press, Cambridge, New York (2007)

    MATH  Google Scholar 

  25. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1), 259–268 (1992)

    Article  MathSciNet  Google Scholar 

  26. Sapiro, G., Ringach, D.L.: Anisotropic diffusion of multivalued images with applications to color filtering. IEEE Trans. Image Process. 5(11), 1582–1586 (1996)

    Article  Google Scholar 

  27. Sereno, M.I., Lutti, A., Weiskopf, N., Dick, F.: Mapping the human cortical surface by combining quantitative T1 with retinotopy. Cereb. Cortex 23(9), 2261–2268 (2013)

    Article  Google Scholar 

  28. Sigalovsky, I.S., Fischl, B., Melcher, J.R.: Mapping an intrinsic MR property of gray matter in auditory cortex of living humans: a possible marker for primary cortex and hemispheric differences. NeuroImage 32(4), 1524–1537 (2006)

    Article  Google Scholar 

  29. Tofts, P.S., et al.: Sources of variation in multi-centre brain MTR histogram studies: Body-coil transmission eliminates inter-centre differences. Magn. Reson. Mater. Phys. 19(4), 209–222 (2006). https://doi.org/10.1007/s10334-006-0049-8

    Article  MathSciNet  Google Scholar 

  30. Tofts, P.S.: Quantitative MRI of the Brain, 1st edn. Wiley, Hoboken (2003)

    Book  Google Scholar 

  31. Tofts, P.S., Steens, S.C.A., van Buchem, M.A.: MT: magnetization transfer. In: Quantitative MRI of the Brain, pp. 257–298. Wiley, Hoboken (2003)

    Google Scholar 

  32. Weiskopf, N., Callaghan, M.F., Josephs, O., Lutti, A., Mohammadi, S.: Estimating the apparent transverse relaxation time (R2*) from images with different contrasts (ESTATICS) reduces motion artifacts. Front. Neurosci. 8, 278 (2014)

    Article  Google Scholar 

  33. Weiskopf, N., et al.: Quantitative multi-parameter mapping of R1, PD*, MT, and R2* at 3T: a multi-center validation. Front. Neurosci. 7, 95 (2013)

    Article  Google Scholar 

  34. Xu, Z., Li, Y., Axel, L., Huang, J.: Efficient preconditioning in joint total variation regularized parallel MRI reconstruction. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9350, pp. 563–570. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24571-3_67

    Chapter  Google Scholar 

Download references

Acknowledgements

YB, MFC and JA were funded by the MRC and Spinal Research Charity through the ERA-NET Neuron joint call (MR/R000050/1). MB and JA were funded by the EU Human Brain Project’s Grant Agreement No 785907 (SGA2). MB was funded by the EPSRC-funded UCL Centre for Doctoral Training in Medical Imaging (EP/L016478/1) and the Department of Health NIHR-funded Biomedical Research Centre at University College London Hospitals. CL is supported by an MRC Clinician Scientist award (MR/R006504/1). The Wellcome Centre for Human Neuroimaging is supported by core funding from the Wellcome [203147/Z/16/Z].

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yaël Balbastre .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Balbastre, Y., Brudfors, M., Azzarito, M., Lambert, C., Callaghan, M.F., Ashburner, J. (2020). Joint Total Variation ESTATICS for Robust Multi-parameter Mapping. In: Martel, A.L., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2020. MICCAI 2020. Lecture Notes in Computer Science(), vol 12262. Springer, Cham. https://doi.org/10.1007/978-3-030-59713-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-59713-9_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59712-2

  • Online ISBN: 978-3-030-59713-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics