Abstract
Denoising of Magnetic Resonance images is important for proper visual analysis, accurate parameter estimation, and for further preprocessing of these images. Maximum Likelihood (ML) estimation methods were proved to be very effective in denoising Magnetic Resonance (MR) images. Among the ML based methods, the recently proposed Non Local Maximum Likelihood (NLML) approach gained much attention. In the NLML method, the samples for the ML estimation of the true underlying intensity are selected in a non local way based on the intensity similarity of the pixel neighborhoods. This similarity is generally measured using the Euclidean distance. A drawback of this approach is the usage of a fixed sample size for the ML estimation and, as a result, optimal results cannot be achieved because of over- or under-smoothing. In this work, we propose an NLML estimation method for denoising MR images in which the samples are selected in an adaptive way using the Kolmogorov-Smirnov (KS) similarity test. The method has been tested both on simulated and real data, showing its effectiveness.
Chapter PDF
Similar content being viewed by others
References
Aja-Fernández, S., Alberola-López, C., Westin, C.: Noise and signal estimation in magnitude MRI and rician distributed images:a LMMSE approach. IEEE Trans. Imag. Proc. 17, 1383–1398 (2008)
Aja-Fernández, S., Tristán, A., Alberola-López, C.: Noise estimation in single and multiple coil magnetic resonance data based on statistical models. Magn. Reson. Imaging 27, 1397–1409 (2009)
Bhattacharyaa, A.: On the measure of divergence between two statistical populations defined by their probability distributions. Bull. Calcutta Math. Soc. 35, 99–109 (1943)
Cocosco, C.A., Kollokian, V., Kwan, R.-S., Evans, A.C.: Brainweb: Online interface to a 3D MRI simulated brain database. NeuroImage 5(4), S425 (1997), http://www.bic.mni.mcgill.ca/brainweb/
Gerig, G., Kubler, O., Kikinis, R., Jolesz, F.A.: Nonlinear anisotropic filtering of MRI data. IEEE Trans. Med. Imag. 11(2), 221–232 (1992)
He, L., Greenshields, I.R.: A nonlocal maximum likelihood estimation method for rician noise reduction in MR images. IEEE Trans. Med. Imaging 28, 165–172 (2009)
Manjón, J.V., Carbonell-Caballero, J., Lull, J.J., GarcÃa-MartÃ, G., MartÃ-BonmatÃ, L., Robles, M.: MRI denoising using non local means. Medical Image Analysis 12, 514–523 (2008)
Manjón, J.V., Coupé, P., MartÃ-BonmatÃand, L., Collins, D.L., Robles, M.: Adaptive non local means denoising of MR images with spatially varying noise levels. J. Magn. Reson. Imaging 31, 192–203 (2010)
Rajan, J., Jeurissen, B., Verhoye, M., Van Audekerke, J., Sijbers, J.: Maximum likelihood estimation-based denoising of magnetic resonance images using restricted local neighborhoods. Physics in Medicine and Biology 56, 5221–5234 (2011)
Rajan, J., Poot, D., Juntu, J., Sijbers, J.: Noise measurement from magnitude MRI using local estimates of variance and skewness. Phys. Med. Biol. 55, N441–N449 (2010)
Rajan, J., Poot, D., Juntu, J., Sijbers, J.: Segmentation based noise variance estimation from background mri data. In: Campilho, A., Kamel, M. (eds.) ICIAR 2010, Part I. LNCS, vol. 6111, pp. 62–70. Springer, Heidelberg (2010)
Rice, S.O.: Mathematical analysis of random noise. Bell. Syst. Tech. 23, 282–332 (1944)
Sijbers, J., den Dekker, A.J.: Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magn. Reson. Med. 51(3), 586–594 (2004)
Sijbers, J., den Dekker, A.J., Scheunders, P., Van Dyck, D.: Maximum likelihood estimation of Rician distribution parameters. IEEE Trans. Med. Imag. 17(3), 357–361 (1998)
Sijbers, J., den Dekker, A.J., Verhoye, M., Van Audekerke, J., Van Dyck, D.: Estimation of noise from magnitude MR images. Magn. Reson. Imaging 16(1), 87–90 (1998)
Sijbers, J., Poot, D., den Dekker, A.J., Pintjens, W.: Automatic estimation of the noise variance from the histogram of a magnetic resonance image. Phys. Med. Biol. 52, 1335–1348 (2007)
Wang, Z., Bovik, A., Sheik, H.R., Simoncelli, E.P.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. on Image Pocessing 13, 600–612 (2004)
Wink, A.M., Roerdink, B.T.M.: BOLD noise assumptions in fMRI. International Journal of Biomedical Imaging 2006, 1–11 (2006)
Zimmer, S., Didas, S., Weickert, J.: A rotationally invariant block matching strategy improving image denoising with non-local means. In: International Workshop on Local and Non-Local Approximation in Image Processing, Switzerland, pp. 135–142 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rajan, J., den Dekker, A.J., Juntu, J., Sijbers, J. (2013). A New Nonlocal Maximum Likelihood Estimation Method for Denoising Magnetic Resonance Images. In: Maji, P., Ghosh, A., Murty, M.N., Ghosh, K., Pal, S.K. (eds) Pattern Recognition and Machine Intelligence. PReMI 2013. Lecture Notes in Computer Science, vol 8251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45062-4_62
Download citation
DOI: https://doi.org/10.1007/978-3-642-45062-4_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45061-7
Online ISBN: 978-3-642-45062-4
eBook Packages: Computer ScienceComputer Science (R0)