A variational model for the restoration of MR images corrupted by blur and Rician noise

Authors:
Pascal Getreuer;Melissa Tong;Luminita A. Vese
Affiliations:
Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan;Department of Mathematics, University of California, Los Angeles;Department of Mathematics, University of California, Los Angeles
Venue:
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part I
Year:
2011

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Abstract

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 L2 and Sobolev (H1) 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.