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T 2 maximum likelihood estimation from multiple spin‐echo magnitude images
Author(s) -
Bonny JeanMarie,
Zanca Michel,
Boire JeanYves,
Veyre Annie
Publication year - 1996
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.1910360216
Subject(s) - magnitude (astronomy) , mathematics , logarithm , monte carlo method , statistics , echo (communications protocol) , gaussian , standard deviation , noise (video) , algorithm , physics , mathematical analysis , artificial intelligence , computer science , image (mathematics) , computer network , quantum mechanics , astronomy
Abstract An optimal maximum likelihood (ML) method is described for an unbiased estimation of monoexponential T 2 from magnitude spin‐echo images. The algorithm is based on a Gaussian assumption of noise distribution. The validity of this assumption was checked by a statistical x 2 test on spin‐echo and fast low‐angle shot surface coil images. Monte‐Carlo simulations of magnitude data showed that the ML estimate standard deviation is lower than that produced by a weighted leastsquares fitting on signal logarithm. Correction schemes are proposed to reduce bias deriving from magnitude reconstruction. The variance of the ML estimate converged rapidly toward the theoretical algebraic expression of the Cramér‐Rao lower bound.