Temporal and Volumetric Denoising via Quantile Sparse Image (QuaSI) Prior in Optical Coherence Tomography and Beyond

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 image modalities. We demonstrate its effectivness on volumetric optical coherence tomography (OCT) and computed tomography (CT) data, which show differnt 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 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 fascilitated through use of an alternating direction method of multipliers (ADMM) scheme and the linearization of the quantile filter. Experiments on multiple dataset emphasize the excellent performance of the proposed method.