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A novel low-rank matrix approximation algorithm for face denoising and background/foreground separation

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Abstract

Low-rank matrix recovery from an observation data matrix has received considerable attention in recent years, which has a wide range of applications in pattern recognition and computer vision, such as face denoising, background/foreground separation, gait recognition, image alignment, etc. However, existing algorithms suffer from the interference of small noise, for example, low-level Gaussian noise, which makes their performance not satisfactory. To address this issue, we are based on the unconstrained nonconvex relaxed minimization model for low-rank and sparse matrices recovery using low-rank matrix decomposition, and propose a novel efficient and effective solving algorithm in terms of direction matrices and step sizes alternating iteration in this paper. The three direction matrices are deduced using Newton method, Taylor expansion and so forth, and the appropriate step size of the direction sparse matrix is searched by the nonmonotonous step size linear search technique efficiently. In theory, we provide the convergence theorem of the proposed algorithm. Experimentally, its efficiency and effectiveness are illustrated under appropriate conditions.

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Notes

  1. http://vision.ucsd.edu/content/extended-yale-face-database-b-b/

  2. http://backgroundmodelschallenge.eu/

  3. http://changedetection.net/

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Acknowledgements

The author would like to thank General Project of Science and Technology Plan of Beijing Municipal Commission of Education (Grant KM202011232018), Key Research and Cultivation Project of Scientific Research on Campus of Beijing Information Science and Technology University (Grant 2021YJPY236) and the reviewers for their valuable suggestions and comments.

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  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Jianxi Zhao

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Correspondence to Jianxi Zhao.

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Communicated by Antonio José Silva Neto.

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Zhao, J. A novel low-rank matrix approximation algorithm for face denoising and background/foreground separation. Comp. Appl. Math. 41, 165 (2022). https://doi.org/10.1007/s40314-022-01871-w

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