Groupwise image registration describes the problem of simultaneously aligning a series of more than two images through individual spatial deformations and it is a common task in the processing of medical image sequences. Variational methods with data fidelity terms based on robust PCA (RPCA) have proven successful in accounting for structural changes in image intensity stemming, e.g., from the uptake of a contrast agent in functional imaging. In this article, we investigate the drawbacks of the most commonly used RPCA data term and derive an improved replacement that employs explicit constraints instead of penalties. We further present a multilevel scheme with theoretically justified scaling to solve the underlying fully deformable registration model. Our numerical experiments on synthetic and real-life medical data confirm the advanced adaptability of RPCA-based data terms and showcase an improved registration accuracy of our algorithm when compared to related groupwise approaches.