T2 maximum likelihood estimation from multiple spin‐echo magnitude images

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Abstract
An optimal maximum likelihood (ML) method is described for an unbiased estimation of monoexponential T2 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 x2 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.