随着稀疏表示在机器学习和图像处理领域中的广泛应用,字典学习的算法受到越来越多的关注。传统意义上训练出来的字典只是一些原子的集合,没有结构。考虑到稀疏表示信号中群结构的稀疏性,建立了基于群稀疏的结构化字典学习的数学模型,并结合凸分析和单调算子理论提出了一个结构化字典学习的有效算法。实验结果表明,该算法具有更快的收敛速度,新模型训练出来的字典能够更好地适应数据,提高表示数据的精度,进而提高图像增强的效果。

Sparse representation of signals is an evolving field in many machine learning and image processing tasks. Nowadays, more and more attention is paid on the algorithm for learning dictionaries.Traditionally, the dictionary is an unstructured set of atoms. Considering the sparsity of the group of the sparse representation signal, a mathematical model of the dictionary learning based on the group sparsity is constructed. We propose an efficient algorithm for learning structured dictionary according to the convex analysis and monotone operator theory. The experiments show that the algorithm converges faster, the dictionary trained from the new model adapts better to the data and the data is better represented, which overall improves the image enhancement effect.