Atlas construction is of great interest in the medical imaging community as a tool to visually and quantitatively characterize anatomic variability within a population. Because such atlases generally exhibit superior data fidelity relative to the individual data sets from which they are constructed, they have also proven invaluable in numerous informatics applications such as automated segmentation and classification, regularization of individual-specific reconstructions from undersampled data, and for characterizing physiologically relevant functional metrics. Perhaps the most valuable role of an anatomic atlas is not to define what is “normal,” but, in fact, to recognize what is “abnormal.” Here, we propose and demonstrate a novel anatomic atlas construction strategy that simultaneously recovers the average anatomy and the deviation from average in a visually meaningful way. The proposed approach treats the problem of atlas construction within the context of robust principal component analysis (RPCA) in which the redundant portion of the data (i.e. the low rank atlas) is separated from the spatially and gradient sparse portion of the data unique to each individual (i.e. the sparse variation). In this paper, we demonstrate the application of RPCA to the Shepp-Logan phantom, including several forms of variability encountered with in vivo data: population variability, class variability, contrast variability, and individual variability. We then present preliminary results produced by applying the proposed approach to in vivo, murine cardiac micro-CT data acquired in a model of right ventricle hypertrophy induced by pulmonary arteriole hypertension.