  Motion estimation of organs in a sequence of images is important in numerous
medical imaging applications. The focus of this paper is the analysis of 4D
Respiratory Correlated Computed Tomography (RCCT) Imaging. It is hypothesized
that the quasi-periodic breathing induced motion of organs in the thorax can be
represented by deformations spanning a very low dimension subspace of the full
infinite dimensional space of diffeomorphic transformations. This paper
presents a novel motion estimation algorithm that includes the constraint for
low-rank motion between the different phases of the RCCT images. Low-rank
deformation solutions are necessary for the efficient statistical analysis and
improved treatment planning and delivery. Although the application focus of
this paper is RCCT the algorithm is quite general and applicable to various
motion estimation problems in medical imaging.
