A Variational Model for the Restoration of MR Images Corrupted by Blur and Rician Noise
In this paper, we propose a variational model to restore images degraded by blur and Rician noise. This model uses total variation regularization with a fidelity term involving the Rician probability distribution. For its numerical solution, we apply and compare the L 2 and Sobolev (H 1) gradient descents, and the iterative method called split Bregman (with a convexified fidelity term). Numerical results are shown on synthetic magnetic resonance imaging (MRI) data corrupted with Rician noise and Gaussian blur, both with known standard deviations.Theoretical analysis of the proposed model is briefly discussed.
KeywordsGradient Descent Gradient Descent Method Convex Approximation Gaussian Blur Total Variation Regularization
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- 4.Neuberger, J.W.: Sobolev gradients and differential equations. Springer Lecture Notes in Mathematics, vol. 1670 (1997)Google Scholar
- 6.Wang, Y., Zhou, H.: Total Variation Wavelet-Based Medical Image Denoising. Hindawi Publishing Corporation International Journal of Biomedical Imaging 2006, 1–6 (2006)Google Scholar
- 8.Wiest-Daesslé, N., Prima, S., Coupé, P., Morrissey, S.P., Barillot, C.: Rician noise removal by non-local means filtering for low signal-to-noise ratio MRI: Applications to DT-MRI. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 171–179. Springer, Heidelberg (2008)CrossRefGoogle Scholar