Naumova Valeriya, Schnass Karin
Simula Metropolitan Center for Digital Engineering, Martin Linges 25, Fornebu, 1325 Norway.
Department of Mathematics, University of Innsbruck, Technikerstraße 13, Innsbruck, 6020 Austria.
EURASIP J Adv Signal Process. 2018;2018(1):12. doi: 10.1186/s13634-018-0533-0. Epub 2018 Feb 22.
This paper extends the recently proposed and theoretically justified iterative thresholding and 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.
本文将最近提出且理论上合理的迭代阈值化与残差均值（ITKrM）算法扩展为从不完整/掩码训练数据中学习字典的算法（ITKrMM）。它进一步使算法适应数据中存在低秩分量的情况，并提供了一种从不完整数据中再次恢复该低秩分量的策略。几个合成实验展示了将关于数据损坏的信息纳入算法的优势。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，并表明该算法在计算复杂度方面或在从损坏数据和未损坏数据中学到的字典之间的一致性方面，与最接近的字典学习对应算法（wKSVD和BPFA）相比具有优势。为了进一步确认所学习字典的适用性，我们探索了其在基于稀疏性的图像修复中的应用。在该应用中，ITKrMM字典表现出与wKSVD和BPFA等其他学习字典相似的性能，并且优于其他基于预定义/解析字典的算法。
