Nuclear Diffusion Models for Low-Rank Background Suppression in Videos

arXiv cs.CV / 4/27/2026

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Key Points

The paper addresses how video restoration can be hindered by structured noise and background artifacts that obscure the underlying dynamic content.
It argues that classic robust principal component analysis (RPCA) struggles because its sparsity assumption may not match the complex variability found in real videos.
The authors propose “Nuclear Diffusion,” a hybrid approach that combines low-rank temporal modeling with diffusion posterior sampling to better represent video structure over time.
Experiments on a real medical imaging task—cardiac ultrasound dehazing—show improved restoration versus RPCA, with gains in contrast enhancement (gCNR) and signal preservation (KS statistic).
The findings suggest that combining model-based temporal priors with deep generative (diffusion) priors can produce higher-fidelity video restoration results.

Abstract

Video sequences often contain structured noise and background artifacts that obscure dynamic content, posing challenges for accurate analysis and restoration. Robust principal component methods address this by decomposing data into low-rank and sparse components. Still, the sparsity assumption often fails to capture the rich variability present in real video data. To overcome this limitation, a hybrid framework that integrates low-rank temporal modeling with diffusion posterior sampling is proposed. The proposed method, Nuclear Diffusion, is evaluated on a real-world medical imaging problem, namely cardiac ultrasound dehazing, and demonstrates improved dehazing performance compared to traditional RPCA concerning contrast enhancement (gCNR) and signal preservation (KS statistic). These results highlight the potential of combining model-based temporal models with deep generative priors for high-fidelity video restoration.