  This paper introduces an universal and structure-preserving regularization
term, called quantile sparse image (QuaSI) prior. The prior is suitable for
denoising images from various medical imaging modalities. We demonstrate its
effectiveness on volumetric optical coherence tomography (OCT) and computed
tomography (CT) data, which show different noise and image characteristics. OCT
offers high-resolution scans of the human retina but is inherently impaired by
speckle noise. CT on the other hand has a lower resolution and shows
high-frequency noise. For the purpose of denoising, we propose a variational
framework based on the QuaSI prior and a Huber data fidelity model that can
handle 3-D and 3-D+t data. Efficient optimization is facilitated through the
use of an alternating direction method of multipliers (ADMM) scheme and the
linearization of the quantile filter. Experiments on multiple datasets
emphasize the excellent performance of the proposed method.
