Abstract
Robust Principal Component Analysis (RPCA) is widely used for low-rank matrix recovery, which restores low-rank structures in damaged data through matrix decomposition. Existing approaches adopt the nuclear norm as a convex approximation of rank function. However, the nuclear norm treats the different singular values equally, leading to suboptimal matrix representation. To better depict the low-rank part, in this paper, we adopt a better surrogate of rank function, namely Schatten Capped p regularization. Further, the Schatten Capped p regularization-based RPCA model is proposed. And then we propose an efficient Alternating Direction Method of Multiplier (ADMM) algorithm to solve for the resulting optimization model. Experimentally, our algorithm is compared to state-of-the-art methods in practical applications such as image denoising, video background and foreground separation, and face de-shadowing. Especially, our algorithm can separate the noise better than other algorithms in the case of low noise levels in image denoising.
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Acknowledgements
Our work was supported by the project of the key research and development ecological conservation and highquality development of the Yellow River Basin Science and Technology of NingXia (No. 2022BEG03165), National Natural Science Foundation of China (Grant Numbers 12071380, 11971374, 12201505).
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Yang, L., Zhang, B., Feng, Q., Liu, X., Wang, J. (2024). Schatten Capped p Regularization for Robust Principle Component Analysis. In: Sheng, B., Bi, L., Kim, J., Magnenat-Thalmann, N., Thalmann, D. (eds) Advances in Computer Graphics. CGI 2023. Lecture Notes in Computer Science, vol 14498. Springer, Cham. https://doi.org/10.1007/978-3-031-50078-7_3
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