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Variance stabilization for Rician-distributed data and its application to noise estimation and removal in MR imaging

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.
Further, we present a stable and fast iterative procedure for robustly estimating the noise level from a single Rician-distributed image. At each iteration, the procedure exploits variance-stabilization composed with a homoskedastic variance-estimation algorithm.
Theoretical and experimental study demonstrates the success of our approach to Rician noise estimation and removal through variance stabilization. In particular, we show that the performance of current state-of-the-art algorithms specifically designed for Rician-distributed data can be matched by combining conventional algorithms designed for additive white Gaussian noise with optimal variance-stabilizing transformations.



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Variance-stabilization of Rician-distributed data new
for Matlab (ver. 7.5 or later)

download zip package

3.6-Mbyte zip-file
includes functions for variance-stabilization, exact unbiased inversion, and noise-level estimation, as well as the complete denoising framework based on these functions.

v1.21, released May 17, 2016

Any unauthorized use of the provided software and files for industrial or profit-oriented activities is expressively prohibited. By downloading any of the files contained in this site, you implicitly agree to all the terms of the TUT limited license. Please read the TUT limited license PDF before you proceed with downloading any of the files.

Links Links

  BM4D algorithm for volumetric data denoising (with Matlab software) new
  Optimized blockwise NL-means with wavelet mixing for Gaussian and Rician volumetric data (with Matlab software)

References References

PDFA. Foi, “Noise Estimation and Removal in MR Imaging: the Variance-Stabilization Approach”, Proc. 2011 IEEE International Symposium on Biomedical Imaging, ISBI 2011, pp. 1809-1814, Chicago (IL), USA, April 2011.  DOI doi:10.1109/ISBI.2011.5872758

PDFM. Maggioni, V. Katkovnik, K. Egiazarian, and A. Foi, “A Nonlocal Transform-Domain Filter for Volumetric Data Denoising and Reconstruction”, IEEE Trans. Image Process., vol. 22, no. 1, pp. 119-133, January 2013.  DOI doi:10.1109/TIP.2012.2210725 software 

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