We introduce a novel image-processing framework for tracking longitudinal changes in white matter microstructure using diffusion tensor imaging (DTI). Charting the trajectory of such temporal changes offers new insight into disease progression but to do so accurately faces a number of challenges. Recent developments have highlighted the importance of processing each subject's data at multiple time points in an unbiased way. In this paper, we aim to highlight a different challenge critical to the processing of longitudinal DTI data, namely the approach to image alignment. Standard approaches in the literature align DTI data by registering the corresponding scalar-valued fractional anisotropy (FA) maps. We propose instead a DTI registration algorithm that leverages full tensor information to drive improved alignment. This proposed pipeline is evaluated against the standard FA-based approach using a DTI dataset from an ongoing study of Alzheimer's disease (AD). The dataset consists of subjects scanned at two time points and at each time point the DTI acquisition consists of two back-to-back repeats in the same scanning session. The repeated scans allow us to evaluate the specificity of each pipeline, using a test–retest design, and assess precision, using bootstrap-based method. The results show that the tensor-based pipeline achieves both higher specificity and precision than the standard FA-based approach. Tensor-based registration for longitudinal processing of DTI data in clinical studies may be of particular value in studies assessing disease progression.