Noise estimation and removal in MR imaging: The variance-stabilization approach

We develop optimal forward and inverse variance-stabilizing transformations for the Rice distribution, in order to approach the problem of magnetic resonance (MR) image filtering by means of standard denoising algorithms designed for homoskedastic observations.

[1]  Pierrick Coupé,et al.  3D Wavelet Subbands Mixing for Image Denoising , 2008, Int. J. Biomed. Imaging.

[2]  D. Louis Collins,et al.  Robust Rician noise estimation for MR images , 2010, Medical Image Anal..

[3]  J. Curtiss.  On Transformations Used in the Analysis of Variance , 1943 .

[4]  Alessandro Foi,et al.  Clipped noisy images: Heteroskedastic modeling and practical denoising , 2009, Signal Process..

[5]  P. L. Meyer.  The Maximum Likelihood Estimate of the Non-Centrality Parameter of a Non-Central χ2 Variate , 1967 .

[6]  Alessandro Foi,et al.  Optimization of variance-stabilizing transformations , 2010 .

[7]  Pierrick Coupé,et al.  Rician Noise Removal by Non-Local Means Filtering for Low Signal-to-Noise Ratio MRI: Applications to DT-MRI , 2008, MICCAI.

[8]  Pierrick Coupé,et al.  An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images , 2008, IEEE Transactions on Medical Imaging.

[9]  Alessandro Foi,et al.  Optimal Inversion of the Anscombe Transformation in Low-Count Poisson Image Denoising , 2011, IEEE Transactions on Image Processing.

[10]  G. Watson.  Bessel Functions. (Scientific Books: A Treatise on the Theory of Bessel Functions) , 1923 .

[11]  Shaul K. Bar-Lev,et al.  ON THE CONSTRUCTION OF CLASSES OF VARIANCE STABILIZING TRANSFORMATIONS , 1990 .

[12]  G. A. Watson.  A treatise on the theory of Bessel functions , 1944 .

[13]  Cheng Guan Koay,et al.  Analytically exact correction scheme for signal extraction from noisy magnitude MR signals. , 2006, Journal of magnetic resonance.