The study evaluates four physically motivated constraints in the estimation of the proton density fat fraction (PDFF). Least squares approaches were developed for constraining the parameters in PDFF quantification based on the physics of magnetic resonance imaging. These were smooth fieldmap, smooth initial phase, nonnegative proton density and moderate R2∗ values. The constraints were evaluated in terms of their influence on the bias and standard deviation of the estimated parameters using numerical simulations and in vivo data acquired at 0.35 T. Results show that unconstrained least squares estimation is noisy and biased and that constraints can be effective at reducing both the standard deviation and bias.
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