MRI: Magnetic Resonance Q-Space Imaging Using Generating Function and Bayesian Inference

Diffusional kurtosis imaging provides the kurtosis for the diffusion displacement of water molecules in vivo. Kurtosis-related metrics demonstrate high sensitivities in several disease diagnoses; however, they contain large systematic and statistical errors. The systematic error can be caused by the truncation of series expansions of the generating functions used for fitting to provide the diffusion parameters, and the cause of the statistical error is overfitting. If we increase the truncation order to reduce the systematic error, overfitting becomes increasingly severe. Hence, a Bayesian approach is developed, in which the arbitrariness regarding the determination of the posterior distributions or the regularization parameter is excluded as much as possible. The Bayesian approach effectively prevents overfitting and reduces imaging noise in kurtosis maps, thereby enabling the use of higher-order terms in the fitting. Our simulation shows that the use of higher-order terms reduced truncation-derived systematic errors in kurtosis estimation.