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Register a new userTensor Completion via Convolutional Sparse Coding Regularization
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Zhebin Wu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations implicitly assume circular boundary conditions and make it hard to fully exploit the sparsity of the problem as well as the small spatial support of the filters. In this work, we propose a novel stochastic spatial-domain solver, in which a randomized subsampling strategy is introduced during the learning sparse codes. Afterwards, we extend the proposed strategy in conjunction with online learning, scaling the CSC model up to very large sample sizes. In both cases, we show experimentally that the proposed subsampling strategy, with a reasonable selection of the subsampling rate, outperforms the state-of-the-art frequency-domain solvers in terms of execution time without losing the learning quality. Finally, we evaluate the effectiveness of the over-complete dictionary learned from large-scale datasets, which demonstrates an improved sparse representation of the natural images on account of more abundant learned image features.
Video capture is limited by the trade-off between spatial and temporal resolution: when capturing videos of high temporal resolution, the spatial resolution decreases due to bandwidth limitations in the capture system. Achieving both high spatial and temporal resolution is only possible with highly specialized and very expensive hardware, and even then the same basic trade-off remains. The recent introduction of compressive sensing and sparse reconstruction techniques allows for the capture of single-shot high-speed video, by coding the temporal information in a single frame, and then reconstructing the full video sequence from this single coded image and a trained dictionary of image patches. In this paper, we first analyze this approach, and find insights that help improve the quality of the reconstructed videos. We then introduce a novel technique, based on convolutional sparse coding (CSC), and show how it outperforms the state-of-the-art, patch-based approach in terms of flexibility and efficiency, due to the convolutional nature of its filter banks. The key idea for CSC high-speed video acquisition is extending the basic formulation by imposing an additional constraint in the temporal dimension, which enforces sparsity of the first-order derivatives over time.
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