Abstract
Spherical navigators are an attractive approach to motion compensation in Magnetic Resonance Imaging. Because they can be acquired quickly, spherical navigators have the potential to measure and correct for rigid motion during image acquisition (prospectively as opposed to retrospectively). A limiting factor to prospective use of navigators is the time required to estimate the motion parameters. This estimation problem can be separated into a rotational and translational component. Recovery of the rotational motion can be cast as a registration of functions defined on a sphere. Previous methods for solving this registration problem are based on optimization strategies that are iterative and require k-space interpolation. Such approaches have undesirable convergence behavior for prospective use since the estimation complexity depends on both the number of samples and the amount of rotation. We propose and demonstrate an efficient algorithm for recovery of rotational motion using spherical navigators. We decompose the navigator magnitude using the spherical harmonic transform. In this framework, rigid rotations can be recovered from an over-constrained system of equations, leading to a computationally efficient algorithm for prospective motion compensation. The resulting algorithm is compared to existing approaches in simulated and actual navigator data. These results show that the spherical harmonic based estimation algorithm is significantly faster than existing methods and so is suited for prospective motion correction.
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References
Ari, N.: Prospective motion correction with chemically selective spherical navigator echoes for functional magnetic resonance imaging. Dissertation, Wake Forest University (2004)
Biswal, B.B., Hyde, J.S.: Contour-based registration technique to differentiate between task-activated and head motion-induced signal variations in fMRI. Magnetic Resonance in Medicine 38(3), 470–476 (1997)
Chirikjian, G.S., Kyatkin, A.B.: Engineering Applications of NonCommunative Harmonic Analysis. CRC Press, Boca Raton (2001)
Cohen, M.S., Weisskoff, R.M.: Ultra-fast imaging. Magnetic Resonance Imaging 9(1), 1–37 (1991)
Driscoll, J.R., Healy, D.M.: Computing Fourier-transforms and convolutions on the 2-sphere. Advances in Applied Mathematics 15(2), 202–250 (1994)
Edmonds, A.R.: Angular Momentum in Quantum Mechanics. Princeton University Press, Princeton (1960)
Fu, Z.W., Wang, Y., Grimm, R.C., Rossman, P.J., Felmlee, J.P., Riederer, S.J., Ehman, R.L.: Orbital navigator echoes for motion measurements in magnetic-resonance-imaging. Magnetic Resonance in Medicine 34(5), 746–753 (1995)
Goldstein, J.D.: The effect of coordinate system rotations on spherical harmonic expansions - a numerical-method. Journal of Geophysical Research 89(B6), 4413–4418 (1984)
Grouch, M.W., Turner, D.A., Erwin, W.D.: Respiratory gating in magnetic-resonance-imaging - improved image quality over nongated images for equal scan time. Clinical Imaging 15(3), 196–201 (1991)
Healy, D.M., Kostelec, P.J., Rockmore, D.: Towards safe and effective high-order Legendre transforms with applications to FFTs for the 2-sphere. Advances in Computational Mathematics 21(1-2), 59–105 (2004)
Hu, X.P., Kim, S.G.: Reduction of signal fluctuation in functional MRI using navigator echoes. Magnetic Resonance in Medicine 31(5), 495–503 (1994)
Lee, C.C., Jack, C.R., Grimm, R.C., Rossman, P.J., Felmlee, J.P., Ehman, R.L., Riederer, S.J.: Real-time adaptive motion correction in functional MRI. Magnetic Resonance in Medicine 36(3), 436–444 (1996)
Makadia, A., Daniilidis, K.: Direct 3D rotation estimation from spherical images via a generalized shift theorem. In: Proceedings. 2003 IEEE Computer Society Conference Computer Vision and Pattern Recognition, 18-20 June 2003, vol. 2, pp. II–217–224(2003)
Masters, G., Richards-Dinger, K.: On the efficient calculation of ordinary and generalized spherical harmonics. Geophys. J. Int. 135, 307–309 (1998)
Welch, E.B., Manduca, A., Grimm, R.C., Ward, H.A., Jack, C.R.: Spherical navigator echoes for full 3D rigid body motion measurement in MRI. Magnetic Resonance in Medicine 47(1), 32–41 (2002)
Zitova, B., Flusser, J.: Image registration methods: a survey. Image and Vision Computing 21(11), 977–1000 (2003)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Rensselaer (1999)
Collins, D.L., Zijdenbos, A.P., Kollokian, V., Sled, J.G., Kabani, N.J., Holmes, C.J., Evans, A.C.: Design and construction of a realistic digital brain phantom. IEEE Trans. on Medical Imaging 17(3), 463–468 (1998)
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Wyatt, C.L., Ari, N., Kraft, R.A. (2005). Spherical Navigator Registration Using Harmonic Analysis for Prospective Motion Correction. In: Christensen, G.E., Sonka, M. (eds) Information Processing in Medical Imaging. IPMI 2005. Lecture Notes in Computer Science, vol 3565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505730_61
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DOI: https://doi.org/10.1007/11505730_61
Publisher Name: Springer, Berlin, Heidelberg
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