Abstract: With the culmination of digital transformation, the textile industry, as an important component of the manufacturing sector, is gradually moving towards the field of intelligent manufacturing. By introducing advanced digital technologies and automation systems, the textile industry can achieve high efficiency and precision in the production process. The application of automation equipment and robots can reduce human errors and labor costs while improving production efficiency. With continuous technological advancements and changing market demands, the textile industry is facing numerous challenges and opportunities. The advent of big data has led to a significant increase in data volume, which poses a significant burden on intelligent manufacturing. Additionally, the increased volume of image data in particular can lead to compression distortion during the transmission process. To address this, compressing images using sparse representation technology can avoid wastage of resources during transmission. Sparse reconstruction, as the inverse problem of sparse representation, is crucial for accurately restoring the sparse-represented image data without losing the original information.
To enhance the core competitiveness of the textile industry, this paper proposed a VBEM (variational Bayesian expectation maximization)-based consistent constrained dictionary (CCD-VBEM) model for fabric image reconstruction. It addressed the problem of decreased reconstruction performance caused by strong inter-column consistency in traditional sparse Bayesian algorithms. Considering the real-world application scenarios of fabric images, a multi-layer prior sparse Bayesian learning (SBL) model was adopted for modeling, and the VBEM method was used to approximate the posterior distribution. This resulted in the construction of the SBL-VBEM model. However, the reconstruction results of the SBL-VBEM model are still affected by the coherence of the dictionary matrix. To improve the reconstruction results, this paper reduced the inter-column consistency of the dictionary matrix.
To achieve this goal, the paper first obtained a shrinkage factor using the topological structure of the sigmoid function. With the shrinkage factor, the neighborhood interval of the largest off-diagonal entry in the dictionary matrix can be reduced at each iteration of obtaining the consistent constrained dictionary. This effectively reduces the inter-column consistency, thereby improving the quality of the reconstruction results. Finally, the obtained consistent constrained dictionary was used as input for the SBL-VBEM model to reconstruct fabric images more effectively. The effectiveness of this approach was validated on the Alibaba Cloud Tianchi dataset. Experimental results demonstrate that the CCD-VBEM method achieves optimal performance in reconstructing fabric images at different sampling rates (0.20–0.40), showcasing the potential of the algorithm in the field of fabric image reconstruction.

Key words: fabric image, reconstruction, consistent constrained dictionary, variational Bayesian expectation maximization, shrinkage factor

摘要： 针对传统稀疏贝叶斯算法中字典列之间较强的相互一致性导致的重构性能下降问题，提出了一种基于变分贝叶斯期望最大化(Variational Bayesian expectation maximization，VBEM)的一致受限字典织物图像重构模型(CCD-VBEM)。考虑织物图像的真实应用场景，采用多层先验的稀疏贝叶斯学习(SBL)模型进行建模，并通过VBEM方法求解后验分布近似值，从而构建SBL-VBEM模型。但SBL-VBEM模型的重构结果仍然受字典矩阵的相关性影响，因此通过减少字典列之间的相互一致性来改善重构结果。首先，通过S形函数的拓扑结构获得收缩因子；然后，在获取一致受限字典的每次迭代中，利用收缩因子缩小字典矩阵中最大非对角项的邻域间隔；最后，将获取的一致受限字典作为SBL-VBEM模型的输入，获得更有效的重构织物图像。对CCD-VBEM模型在阿里云天池数据集上进行验证，验证结果表明，在不同采样率（0.20~0.40）下，CCD-VBEM模型对织物图像的重构均获得最优性能。

关键词: 织物图像, 重构, 一致受限字典, 变分贝叶斯期望最大化, 收缩因子