Parameterized Low-Rank Regularizer for High-dimensional Visual Data

Factorization models and nuclear norms, two prominent methods for characterizing the low-rank prior, encounter challenges in accurately retrieving low-rank data under severe degradation and lack generalization capabilities. To mitigate these limitations, we propose a Parameterized Low-Rank Regularizer (PLRR), which models low-rank visual data through matrix factorization by utilizing neural networks to parameterize the factor matrices, whose feasible domains are essentially constrained. This approach can be interpreted as imposing an automatically learned penalty on factor matrices. More significantly, the knowledge encoded in network parameters enhances generalization. As a versatile low-rank modeling tool, PLRR exhibits superior performance in various inverse problems, including video foreground extraction, hyperspectral image (HSI) denoising, HSI inpainting, multi-temporal multispectral image (MSI) decloud, and MSI guided blind HSI super-resolution. More significantly, PLRR demonstrates robust generalization capabilities for images with diverse degradations, temporal variations, and scene contexts.