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Robust principal component analysis via weighted nuclear norm with modified second-order total variation regularization

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Abstract

The traditional robust principal component analysis (RPCA) model aims to decompose the original matrix into low-rank and sparse components and uses the nuclear norm to describe the low-rank prior information of the natural image. In addition to low-rankness, it has been found in many recent studies that local smoothness is also crucial prior in low-level vision. In this paper, we propose a new RPCA model based on weight nuclear norm and modified second-order total variation regularization (WMSTV-RPCA for short), which exploits both the global low-rankness and local smoothness of the matrix. Extensive experimental results show, both qualitatively and quantitatively, that the proposed WMSTV-RPCA can more effectively remove noise, and model dynamic scenes compared with the competing methods.

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Data availability statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. College of Computer and Information Science, Southwest University, Chongqing, China

    Yi Dou

  2. School of Mathematics and Statistics, Southwest University, Chongqing, China

    **nling Liu & Jianjun Wang

  3. Information Construction Office, Southwest University, Chongging, China

    Min Zhou

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  1. Yi Dou
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  2. **nling Liu
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  3. Min Zhou
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  4. Jianjun Wang
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Correspondence to Jianjun Wang.

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Dou, Y., Liu, X., Zhou, M. et al. Robust principal component analysis via weighted nuclear norm with modified second-order total variation regularization. Vis Comput 39, 3495–3505 (2023). https://doi.org/10.1007/s00371-023-02960-5

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