Sparse Adaptive Optimization Based on Low Rank Decomposition for Image Defect Detection

Low-rank optimization plays a pivotal role in image processing due to its inherent ability to capture low-dimensional structures and promote sparsity. Traditional low-rank decomposition methods aim to recover low-rank components and isolate sparse elements, but the structural integrity of the sparse components is often compromised. Moreover, the interplay between low-rank and sparse terms can lead to conflicting effects in practical scenarios. To address these limitations, this paper proposes a novel low-rank decomposition model that introduces a new form of regularization, effectively balancing low-rank representation and structured sparsity. The proposed model enhances the structural expressiveness of the sparse component while preserving the global low-rank structure. To solve the resulting optimization problem efficiently, we develop a tailored algorithm based on operator splitting techniques, significantly improving computational efficiency without sacrificing accuracy. Extensive experiments on tasks such as defect detection and background reconstruction demonstrate that the proposed method outperforms existing approaches, achieving superior accuracy and robustness across various real-world scenarios.