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Maximum likelihood estimation of signal amplitude and noise variance from MR data
Author(s) -
Sijbers J.,
den Dekker A.J.
Publication year - 2004
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.10728
Subject(s) - gaussian noise , noise (video) , magnitude (astronomy) , amplitude , data set , gaussian , mathematics , algorithm , signal (programming language) , statistics , computer science , artificial intelligence , image (mathematics) , physics , programming language , quantum mechanics , astronomy
Abstract In MRI, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian‐distributed noise. After applying an inverse Fourier transform, the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets. This article addresses the question whether it is better to use complex valued data or magnitude data for the estimation of these parameters using the maximum likelihood method. As a performance criterion, the mean‐squared error (MSE) is used. Magn Reson Med 51:586–594, 2004. © 2004 Wiley‐Liss, Inc.