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IPI

Diffusion Kurtosis Imaging (DKI) is a new Magnetic
Resonance Imaging (MRI) model to characterize the non-Gaussian
diffusion behavior in tissues. In reality, the term
$bD_{app}-\frac{1}{6}b^2D_{app}^2K_{app}$ in the extended Stejskal
and Tanner equation of DKI should be positive for an appropriate range of $b$-values
to make sense
physically. The positive definiteness of the above term reflects the
signal attenuation in tissues during imaging. Hence, it is essential
for the validation of DKI.

In this paper, we analyze the positive definiteness of DKI. We first characterize the positive definiteness of DKI through the positive definiteness of a tensor constructed by diffusion tensor and diffusion kurtosis tensor. Then, a conic linear optimization method and its simplified version are proposed to handle the positive definiteness of DKI from the perspective of numerical computation. Some preliminary numerical tests on both synthetical and real data show that the method discussed in this paper is promising.

In this paper, we analyze the positive definiteness of DKI. We first characterize the positive definiteness of DKI through the positive definiteness of a tensor constructed by diffusion tensor and diffusion kurtosis tensor. Then, a conic linear optimization method and its simplified version are proposed to handle the positive definiteness of DKI from the perspective of numerical computation. Some preliminary numerical tests on both synthetical and real data show that the method discussed in this paper is promising.

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