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Adaptive optimization of low rank decomposition and its application on fabric defect detection

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Abstract

In practical applications of fabric defect detection, low-rank decomposition is the effective method. Sparse matrices represent defect results, so sparse terms are the focus of this application. Because the characteristics of each observation matrix differ, the weight of sparse term also differ. Therefore, this paper proposes adaptive weight for the model, allowing it to find suitable weight for different observation matrices and thereby improving the accuracy of model. During the matrix separation process of the model, elements that should belong to the sparse matrix may be separated into the noise matrix. To address this, this paper establishes new constraints to achieve a deeper separation between the two. While establishing the corresponding algorithmic framework, this paper also considers the fluctuations in the model’s solution process and proposes a new definition for the penalty factors. This aims to improve algorithm efficiency and reduce CPU time. This paper also provides a convergence analysis of the proposed method. In the dataset of fabric defects, it was shown that the star and dot types had the best results in TPR and F-measure, with TPR of 85.15% and 81.56%, and f-measure of 70.51% and 65.40%, respectively. Indicating that the method proposed in this paper has the fastest calculation speed.

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Code availability

The datasets generated during and/or analysed during the current study are available in the [Industrial Automation Research Laboratory from Department of Electrical and Electronic Engineering of Hong Kong University] repository, [https://lmb.informat-ik.unifreiburg.de/resources/datasets/tilda.en.html].

The code of our algorithm will upload to github, than the name of the repository is [Chen-ZX07/low-rank-defect_detection].

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Acknowledgements

Thanks to Professor Liu Hao for her suggestions on revisions during the paper review process;

Thanks to the National Natural Science Foundation of China [grant numbers 12201075] for providing funding projects.

Funding

The first author is supported by [National Natural Science Foundation of China] (Grant numbers [12201075] ); The fourth author is supported by [the Xuzhou Science and Technology Plan Project] (Grant numbers [KC23416]).

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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Jiuzhen Liang], [Wenya Shi], [Zhixiang Chen] and [Daihong Jiang]. The first draft of the manuscript was written by [Zhixiang Chen] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Zhixiang Chen or Jiuzhen Liang.

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Shi, W., Chen, Z., Liang, J. et al. Adaptive optimization of low rank decomposition and its application on fabric defect detection. Pattern Anal Applic 28, 4 (2025). https://doi.org/10.1007/s10044-024-01363-z

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