Robust Estimation of Kurtosis and Diffusion Tensors in Diffusional Kurtosis Imaging

Ali Tabesh¹, Jens H. Jensen¹, Babak A. Ardekani², Joseph A. Helpern^1,2

The diffusional kurtosis imaging model of non-Gaussian water diffusion is parameterized by the diffusion and kurtosis tensors, which are typically estimated via unconstrained least squares (LS) methods. Unfortunately, these methods do not necessarily produce physically and biologically plausible tensor estimates. We address this drawback by formulating the estimation problem as linearly constrained linear LS. Comparison of in vivo mean kurtosis maps obtained using the proposed formulation and unconstrained linear LS highlights the improved estimation quality. The proposed formulation achieves comparable map quality with fewer gradient images than the unconstrained LS approach, offering a savings of 38% in acquisition time.