Abstract
Recent research on magnitude Magnetic Resonance Images (MRI) reconstruction from the Fourier inverse transform of complex (gaussian contaminated) data sets focuses on the proper modeling of the resulting Rician noise contaminated data. In this paper we consider a variational Rician denoising model for MRI data sets that we solve by a semi-implicit numerical scheme, which leads to the resolution of a sequence of Rudin, Osher and temi (ROF) models. The (iterated) resolution of these well posed numerical problems is then proposed for Total Variation (TV) Rician denoising. For numerical comparison we also consider a direct semi-implicit approach for the primal problem which amounts to consider some (regularizing) approximating problems. Synthetic and real MR brain images are then denoised and the results show the effectiveness of the new method in both, the accuracy and the speeding up of the algorithm.
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References
Henkelman, R.M.: Measurement of signal intensities in the presence of noise in MR images. Med. Phys. 12(2), 232–233 (1985)
Gudbjartsson, H., Patz, S.: The Rician distribution of noisy MRI data. J. of Magn. Reson. Med. 34(6), 910–914 (1995)
Sijbers, J., Den Dekker, A.J., Van Audekerke, J., Verhoye, M., Van Dyck, D.: Estimation of the noise in magnitude MR images. Magn. Reson. Imaging 16(1), 87–98 (1998)
Martín, A., Garamendi, J.F., Schiavi, E.: Iterated Rician Denoising. In: Proceedings of the International Conference on Image Processing, Computer Vision and Pattern Recognition, IPCV 2011, pp. 959–963. CSREA Press, Las Vegas (2011)
Getreuer, P., Tong, M., Vese, L.A.: A Variational Model for the Restoration of MR Images Corrupted by Blur and Rician Noise. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Wang, S., Kyungnam, K., Benes, B., Moreland, K., Borst, C., DiVerdi, S., Yi-Jen, C., Ming, J. (eds.) ISVC 2011, Part I. LNCS, vol. 6938, pp. 686–698. Springer, Heidelberg (2011)
Basu, S., Fletcher, T., Whitaker, R.T.: Rician Noise Removal in Diffusion Tensor MRI. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006, Part I. LNCS, vol. 4190, pp. 117–125. Springer, Heidelberg (2006)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)
Chambolle, A.: An algorithm for Total variation Minimization and Applications. J. of Mathematical Imaging and Vision 20, 89–97 (2004)
Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University (2000)
Lassey, K.R.: On the Computation of Certain Integrals Containing the Modified Bessel Function I 0(ξ). J. of Mathematics of Computation 39(160), 625–637 (1982)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on PAMI 12(7), 629–639 (1990)
Nikolova, M., Esedoglu, S., Chan, T.F.: Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models. SIAM Journal of Applied Mathematics 66(5), 1632–1648 (2006)
Aubert-Broche, B., Griffin, M., Pike, G., Evans, A., Collins, D.: Twenty New Digital Brain Phantoms for Creation of Validation Image Data Bases. IEEE Transactions on Medical Imaging 24(11), 1410–1416 (2006)
Jones, D.K., Horsfield, M.A., Simmons, A.: Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging. J. of Magn. Reson. Med. 42(3), 515–525 (1999)
Casas, E., Kunisch, K., Pola, C.: Some applications of BV functions in optimal control and calculus of variations. ESAIM: Proceedings. Control and Partial Differential Equations 4, 83–96 (1998)
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Martin, A., Garamendi, JF., Schiavi, E. (2013). MRI TV-Rician Denoising. In: Gabriel, J., et al. Biomedical Engineering Systems and Technologies. BIOSTEC 2012. Communications in Computer and Information Science, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38256-7_17
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DOI: https://doi.org/10.1007/978-3-642-38256-7_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38255-0
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