  Longitudinal MRI is an important diagnostic imaging tool for evaluating the
effects of treatment and monitoring disease progression. However, MRI, and
particularly longitudinal MRI, is known to be time consuming. To accelerate
imaging, compressed sensing (CS) theory has been applied to exploit sparsity,
both on single image as on image sequence level. State-of-the-art CS methods
however, are generally focused on image reconstruction, and consider analysis
(e.g., alignment, change detection) as a post-processing step.
  In this study, we propose DELTA-MRI, a novel framework to estimate
longitudinal image changes {\it directly} from a reference image and
subsequently acquired, strongly sub-sampled MRI k-space data. In contrast to
state-of-the-art longitudinal CS based imaging, our method avoids the
conventional multi-step process of image reconstruction of subsequent images,
image alignment, and deformation vector field computation. Instead, the set of
follow-up images, along with motion and deformation vector fields that describe
their relation to the reference image, are estimated in one go. Experiments
show that DELTA-MRI performs significantly better than the state-of-the-art in
terms of the normalized reconstruction error.
