Error Bounds For Semi-Parametric Estimation in MRS
Capobianco E, Ratiney H, van Ormondt D, de Beer R, Graveron-Demilly D
University of Boston
The presence of a non-parametric background in 1H short echo-time signals invalidates the theory of Cramer-Rao lower Bounds (CRBs) on metabolite estimation errors. As a result, the usual CRBs, derived in absence of background, become unattainable. The increase of the metabolite estimation errors depends on the way of handling a non-parametric background. Seeking alternative lower bounds for each of the many *ways* of handling non-parametric backgrounds is impractical. We improve the situation by deriving a simple, general expression of CRBs that encompasses unconstrained estimation of the initial part of the background signal that is above the noise level.