Abstract
Certain MRI acquisitions, such as Sodium imaging, produce data with very low signal-to-noise ratio (SNR). One approach to improve SNR is to acquire several images, each of which takes may take more than a minute, and then average these measurements. A consequence of such a lengthy acquisition procedure is subject motion between each image. This work investigates a solution for retrospective motion correction in this scenario, where the high level of Rician noise renders standard registration tools less effective. We employ a simple generative model for the data based on tissue segmentation maps, and provide a differentiable approximation of the Rician log-likelihood to fit the model to the observations. We find that this approach substantially outperforms a Gaussian log-likelihood baseline on synthetic data that has been corrupted by Rician noise of varying degrees. We also provide results of our approach on real Sodium MRI data, and demonstrate that we can reduce the effects of substantial motion compared to a general purpose registration tool.
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References
Ashburner, J., Friston, K.J.: Unified segmentation. Neuroimage 26(3), 839–851 (2005)
Ashburner, J., Neelin, P., Collins, D., Evans, A., Friston, K.: Incorporating prior knowledge into image registration. Neuroimage 6(4), 344–352 (1997)
Avants, B.B., Tustison, N., Song, G., et al.: Advanced normalization tools (ants). Insight j 2(365), 1–35 (2009)
Balakrishnan, G., Zhao, A., Sabuncu, M.R., Guttag, J., Dalca, A.V.: VoxelMorph: a learning framework for deformable medical image registration. IEEE Trans. Med. Imaging 38(8), 1788–1800 (2019)
Boyd, S., Boyd, S.P., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Gudbjartsson, H., Patz, S.: The Rician distribution of noisy MRI data. Magn. Reson. Med. 34(6), 910–914 (1995)
Hoffman, M.D., Blei, D.M., Wang, C., Paisley, J.: Stochastic variational inference. J. Mach. Learn. Res. 14(40), 1303–1347 (2013). https://jmlr.org/papers/v14/hoffman13a.bib
Jenkinson, M., Bannister, P., Brady, M., Smith, S.: Improved optimization for the robust and accurate linear registration and motion correction of brain images. Neuroimage 17(2), 825–841 (2002)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Klein, S., Staring, M., Murphy, K., Viergever, M.A., Pluim, J.P.: Elastix: a toolbox for intensity-based medical image registration. IEEE Trans. Med. Imaging 29(1), 196–205 (2009)
Madelin, G., Regatte, R.R.: Biomedical applications of sodium MRI in vivo. J. Magn. Reson. Imaging 38(3), 511–529 (2013)
Manjón, J.V., Carbonell-Caballero, J., Lull, J.J., García-Martí, G., Martí-Bonmatí, L., Robles, M.: MRI denoising using non-local means. Med. Image Anal. 12(4), 514–523 (2008)
Ourselin, S., Roche, A., Subsol, G., Pennec, X., Ayache, N.: Reconstructing a 3D structure from serial histological sections. Image Vis. Comput. 19(1–2), 25–31 (2001)
Paszke, A., et al.: Automatic differentiation in PyTorch (2017)
Pipe, J.G., Zwart, N.R., Aboussouan, E.A., Robison, R.K., Devaraj, A., Johnson, K.O.: A new design and rationale for 3D orthogonally oversampled k-space trajectories. Magn. Reson. Med. 66(5), 1303–1311 (2011)
Ramos-Llordén, G., Arnold, J., Van Steenkiste, G., Van Audekerke, J., Verhoye, M., Sijbers, J.: Simultaneous motion correction and t1 estimation in quantitative t1 mapping: an ml restoration approach. In: 2015 IEEE International Conference on Image Processing (ICIP), pp. 3160–3164. IEEE (2015)
Reuter, M., Rosas, H.D., Fischl, B.: Highly accurate inverse consistent registration: a robust approach. Neuroimage 53(4), 1181–1196 (2010)
Riemer, F., Solanky, B.S., Stehning, C., Clemence, M., Wheeler-Kingshott, C.A., Golay, X.: Sodium (23Na) ultra-short echo time imaging in the human brain using a 3D-cones trajectory. Magn. Reson. Mater. Phys., Biol. Med. 27(1), 35–46 (2014)
Rose, A.M., Valdes, R., Jr.: Understanding the sodium pump and its relevance to disease. Clin. Chem. 40(9), 1674–1685 (1994)
Wolfram Mathworld: Modified Bessel function of the first kind. https://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html
Woolrich, M.W., Jenkinson, M., Brady, J.M., Smith, S.M.: Fully Bayesian spatio-temporal modeling of fMRI data. IEEE Trans. Med. Imaging 23(2), 213–231 (2004)
Zwart, N.R., Johnson, K.O., Pipe, J.G.: Efficient sample density estimation by combining gridding and an optimized kernel. Magn. Reson. Med. 67(3), 701–710 (2012)
Acknowledgments
We acknowledge funding from the University of Sussex used in the data acquisition. We thank Guillaume Madelin for providing the Sodium MRI sequence.
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Simpson, I.J.A., Örzsik, B., Harrison, N., Asllani, I., Cercignani, M. (2022). Motion Correction in Low SNR MRI Using an Approximate Rician Log-Likelihood. In: Hering, A., Schnabel, J., Zhang, M., Ferrante, E., Heinrich, M., Rueckert, D. (eds) Biomedical Image Registration. WBIR 2022. Lecture Notes in Computer Science, vol 13386. Springer, Cham. https://doi.org/10.1007/978-3-031-11203-4_16
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