Diffusion Kurtosis Imaging (abbr. DKI) is a Magnetic Resonance Imaging (abbr. MRI) model in medical engineering, which can characterize the non-Gaussian diffusion behavior in tissues. To ensure the physical validity of DKI, the term \(b D \textbf{x}^2 - \frac{1}{6} b^2 M_D^2 \mathscr {W}\textbf{x}^4\) should be positive for all gradient directions \(\textbf{x}\) and a range of diffusion weighted b-values b, which is called the positive definiteness of DKI and reflects the signal attenuation in tissues during imaging. In this paper, we provide the criteria for judging the positive definiteness of DKI and shows that they are practical and effective via numerical examples whose data come from MRI experiments and random generation.
