Biomedical Engineering Reference
In-Depth Information
MRI TV-Rician Denoising
Adrian Martin 1 , 2 , 3 , Juan-Francisco Garamendi 4 , and Emanuele Schiavi 2 , 3
1 Fundaci on CIEN-Fundaci on Reina Sofıa, Madrid, Spain
2 Neuroimaging lab., Univ. Politecnica de Madrid-Univ. Rey Juan Carlos,
Center for Biomedical Technology, Madrid, Spain
3 Departamento de Matematica Aplicada, Universidad Rey Juan Carlos, Madrid, Spain
4 INRIA/INSERM U746/CNRS, UMR6074/University of Rennes I,
VisAGeS Research Team, Rennes, France
{ adrian.martin,emanuele.schiavi } @urjc.es,
juan-francisco.garamendi bragado@inria.fr
Abstract. Recent research on magnitude Magnetic Resonance Images (MRI) re-
construction from the Fourier inverse transform of complex (gaussian contami-
nated) data sets focuses on the proper modeling of the resulting Rician noise con-
taminated 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 (iter-
ated) 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 im-
ages are then denoised and the results show the effectiveness of the new method
in both, the accuracy and the speeding up of the algorithm.
Keywords: MRI Rician denoising, Total variation, Numerical resolution, ROF
model.
1
Introduction
Modelling MRI denoising, a fundamental step in medical image processing, leads natu-
rally to the assumption that MR magnitude images are corrupted by Rician noise which
is a signal dependent noise (see [1], [2] and [3]). In fact this noise is originated in the
computation of the magnitude image from the real and imaginary images, that are ob-
tained from the inverse Fourier Transform applied to the original raw data. This process
involves a non-linear operation which maps the original Gaussian distribution of the
noise to a Rician distribution.
Nevertheless it is usually argued that this bias do not affect seriously the process-
ing and subsequent analysis of MR images and a gaussian noise, identically distributed
and not signal dependent, is modeled. To go beyond the unlikely assumption of gaus-
sian noise, we consider, in a variational framework, a denoising model for MR Rician
noise contaminated images recently considered (independently) in [4] and in [5], which
combines the Total Variation semi-norm with a data fitting term (see also [6] for an ap-
plication to DT-MRI data denoising where low SNR Diffusion Weighted Images (DWI)
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