DELTA-MRI: Direct deformation Estimation from LongiTudinally Acquired k-space data

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.