Reconstructing diffusion kurtosis tensors from sparse noisy measurements

Diffusion kurtosis imaging (DKI) is a recent MRI based method that can quantify deviation from Gaussian behavior using a kurtosis tensor. DKI has potential value for the assessment of neurologic diseases. Existing techniques for diffusion kurtosis imaging typically need to capture hundreds of MRI images, which is not clinically feasible on human subjects. In this paper, we develop robust denoising and model fitting methods that make it possible to accurately reconstruct a kurtosis tensor from 75 or less noisy measurements. Our denoising method is based on subspace learning for multi-dimensional signals and our model fitting technique uses iterative reweighting to effectively discount the influences of outliers. The total data acquisition time thus drops significantly, making diffusion kurtosis imaging feasible for many clinical applications involving human subjects.