Reconstruction of Parametric Maps

Implementation details and properties of these two approaches are discussed in Refs. 23,29,54. 

Obtaining parametric maps necessarily requires estimating the vector of the parameter 0 from K-noised samples. The general theory of estimation59,60 provides solutions that can be applied in the domain of quantitative MRI. In practice, the ML approach is the most commonly used, because it concerns the estimation of non-random parameters, unlike the Bayesian approach, which is mostly applied to segment the images.61 The LS approaches defined by 

As stated above, the utility of the ML estimators derives essentially from their asymptotic properties of consistency and optimality (i.e., cov(0ml) — CRB). When the data exhibits significant departures from theoretical pdf (Gaussian or Rice) owing to acquisition artifacts, it may be judicious to use robust non-linear regression techniques,62 as in parametric diffusion-tensor imaging reconstructed from echo-planar data.63 

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