This paper extends the recently proposed and theoretically justified iterative thresholding and K residual means (ITKrM) algorithm to learning dictionaries from incomplete/masked training data (ITKrMM). It further adapts the algorithm to the presence of a low-rank component in the data and provides a strategy for recovering this low-rank component again from incomplete data. Several synthetic experiments show the advantages of incorporating information about the corruption into the algorithm. Further experiments on image data confirm the importance of considering a low-rank component in the data and show that the algorithm compares favourably to its closest dictionary learning counterparts, wKSVD and BPFA, either in terms of computational complexity or in terms of consistency between the dictionaries learned from corrupted and uncorrupted data. To further confirm the appropriateness of the learned dictionaries, we explore an application to sparsity-based image inpainting. There the ITKrMM dictionaries show a similar performance to other learned dictionaries like wKSVD and BPFA and a superior performance to other algorithms based on pre-defined/analytic dictionaries.

中文翻译：

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从不完整的数据中快速学习字典。

本文将最近提出的、理论上合理的迭代阈值和 K 残差均值 (ITKrM) 算法扩展到从不完整/屏蔽训练数据 (ITKrMM) 中学习字典。它进一步使算法适应数据中低秩分量的存在，并提供从不完整数据中再次恢复该低秩分量的策略。一些综合实验显示了将有关损坏的信息纳入算法的优点。对图像数据的进一步实验证实了考虑数据中低秩分量的重要性，并表明该算法无论是在计算复杂性方面还是在词典之间的一致性方面都优于最接近的词典学习算法 wKSVD 和 BPFA从损坏和未损坏的数据中学习。为了进一步确认学习字典的适当性，我们探索了基于稀疏性的图像修复的应用。ITKrMM 词典显示出与 wKSVD 和 BPFA 等其他学习词典类似的性能，并且比基于预定义/分析词典的其他算法具有优越的性能。