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This paper introduces an universal and structure-preserving regularizationterm, called quantile sparse image (QuaSI) prior. The prior is suitable fordenoising images from various medical imaging modalities. We demonstrate itseffectiveness on volumetric optical coherence tomography (OCT) and computedtomography (CT) data, which show different noise and image characteristics. OCToffers high-resolution scans of the human retina but is inherently impaired byspeckle noise. CT on the other hand has a lower resolution and showshigh-frequency noise. For the purpose of denoising, we propose a variationalframework based on the QuaSI prior and a Huber data fidelity model that canhandle 3-D and 3-D+t data. Efficient optimization is facilitated through theuse of an alternating direction method of multipliers (ADMM) scheme and thelinearization of the quantile filter. Experiments on multiple datasetsemphasize the excellent performance of the proposed method.

Temporal and volumetric denoising via quantile sparse image prior