Quality-preserving low-cost probabilistic 3D denoising with applications to Computed Tomography

We propose a pipeline for a synthetic generation of personalized Computer Tomography (CT) images, with a radiation exposure evaluation and a lifetime attributable risk (LAR) assessment. We perform a patient-specific performance evaluation for a broad range of denoising algorithms (including the most popular Deep Learning denoising approaches, wavelets-based methods, methods based on Mumford-Shah denoising etc.), focusing both on accessing the capability to reduce the patient-specific CT-induced LAR and on computational cost scalability. We introduce a parallel probabilistic Mumford-Shah denoising model (PMS), showing that it markedly-outperforms the compared common denoising methods in denoising quality and cost scaling. In particular, we show that it allows an approximately 22-fold robust patient-specific LAR reduction for infants and a 10-fold LAR reduction for adults. Using a normal laptop the proposed algorithm for PMS allows a cheap and robust (with the Multiscale Structural Similartity index > 90%) denoising of very large 2D videos and 3D images (with over 107 voxels) that are subject to ultra-strong Gaussian and various non-Gaussian noises, also for Signal-to-Noise Ratios much below 1.0. The code is provided for open access. One-sentence summaryProbabilisitc formulation of Mumford-Shah principle (PMS) allows a cheap quality-preserving denoising of ultra-noisy 3D images and 2D videos.