论文标题
通过卷积稀疏编码正则化完成张量
Tensor Completion via Convolutional Sparse Coding Regularization
论文作者
论文摘要
张量数据在获取复杂的高维结构时通常会遇到缺失的价值问题。为了完成丢失的信息，已经提出了许多低级张量完成（LRTC）方法，其中大多数取决于张量数据的低级别属性。通过这种方式，可以大致恢复原始数据的低级别组件。但是，缺点是，无论核定标准的总和（SNN）和张量的核定标准（TNN）方法，细节信息都无法完全恢复。相反，在信号处理领域，卷积稀疏编码（CSC）可以很好地表示图像的高频组件，这通常与数据的详细信息相关联。但是，CSC无法很好地处理低频组件。为此，我们提出了两种新型方法，即LRTC-CSC-I和LRTC-CSC-II，它们采用CSC作为LRTC的补充正规化来捕获高频组件。因此，LRTC-CSC方法不仅可以解决缺失的值问题，还可以恢复细节。此外，由于稀疏性特征，可以用小样本对正规器CSC进行训练。广泛的实验显示了LRTC-CSC方法的有效性，定量评估表明我们的模型的性能优于最新方法。
Tensor data often suffer from missing value problem due to the complex high-dimensional structure while acquiring them. To complete the missing information, lots of Low-Rank Tensor Completion (LRTC) methods have been proposed, most of which depend on the low-rank property of tensor data. In this way, the low-rank component of the original data could be recovered roughly. However, the shortcoming is that the detail information can not be fully restored, no matter the Sum of the Nuclear Norm (SNN) nor the Tensor Nuclear Norm (TNN) based methods. On the contrary, in the field of signal processing, Convolutional Sparse Coding (CSC) can provide a good representation of the high-frequency component of the image, which is generally associated with the detail component of the data. Nevertheless, CSC can not handle the low-frequency component well. To this end, we propose two novel methods, LRTC-CSC-I and LRTC-CSC-II, which adopt CSC as a supplementary regularization for LRTC to capture the high-frequency components. Therefore, the LRTC-CSC methods can not only solve the missing value problem but also recover the details. Moreover, the regularizer CSC can be trained with small samples due to the sparsity characteristic. Extensive experiments show the effectiveness of LRTC-CSC methods, and quantitative evaluation indicates that the performance of our models are superior to state-of-the-art methods.
