Pascal Getreuer, Melissa Tong, and Luminita A. Vese. “A variational model for the restoration of MR images corrupted by blur and Rician noise.” International Symposium on Visual Computing. Springer, Berlin, Heidelberg, 2011. DOI: 10.1007/978-3-642-24028-7_63.

@inproceedings{getreuer2011variational,
title={A variational model for the restoration of {MR} images
corrupted by blur and {Rician} noise},
author={Getreuer, Pascal and Tong, Melissa and Vese, Luminita A},
booktitle={International Symposium on Visual Computing},
pages={686--698},
year={2011},
organization={Springer}
}

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 $$L^2$$ 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.

The final publication is available at https://doi.org/10.1007/978-3-642-24028-7_63