Registration of High Angular Resolution Diffusion MRI Images Using 4 th Order Tensors

Registration of Diffusion Weighted (DW)-MRI datasets has been commonly achieved to date in literature by using either scalar or 2

nd

-order tensorial information. However, scalar or 2

nd

-order tensors fail to capture complex local tissue structures, such as fiber crossings, and therefore, datasets containing fiber-crossings cannot be registered accurately by using these techniques. In this paper we present a novel method for non-rigidly registering DW-MRI datasets that are represented by a field of 4

th

-order tensors. We use the Hellinger distance between the normalized 4

th

-order tensors represented as distributions, in order to achieve this registration. Hellinger distance is easy to compute, is scale and rotation invariant and hence allows for comparison of the true shape of distributions. Furthermore, we propose a novel 4

th

-order tensor re-transformation operator, which plays an essential role in the registration procedure and shows significantly better performance compared to the re-orientation operator used in literature for DTI registration. We validate and compare our technique with other existing scalar image and DTI registration methods using simulated diffusion MR data and real HARDI datasets.