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

• Published in: Pattern analysis and applications : PAA Vol. 28; no. 1
• Main Authors: Shi, Wenya, Chen, Zhixiang, Liang, Jiuzhen, Jiang, Daihong
• Format: Journal Article
• Language: English
• Published: London Springer London 01.03.2025; Springer Nature B.V
• Subjects: Algorithms; Computer Science; Decomposition; Defects; Original Article; Pattern Recognition; Separation; Sparse matrices; Sparsity; Low-rank decomposition; Penalty factor; Constraint conditions; Adaptive weights; Defect detection
• ISSN: 1433-7541; 1433-755X
• DOI: 10.1007/s10044-024-01363-z

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.