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Factorized Tensor Dictionary Learning for Visual Tensor Data Completion
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DOI：10.1109/TMM.2020.2994512.png)
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Abstract
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This paper aims at developing a dictionary-learning-based method for completing the visual tensor data with missing elements. Traditional dictionary learning approaches suffer from very high computational costs when processing high-dimensional tensor data. Some existing approaches for acceleration impose orthogonality constraints or rank-one decompositions on dictionary atoms; however, the expressibility of the resulting dictionary is rather limited. To address such issues, we propose a convolutional analysis model for tensor dictionary learning, where the update of sparse coefficients during dictionary learning is simple and fast. Furthermore, we propose an orthogonality-constrained convolutional factorization scheme for dictionary construction, in which each tensor dictionary atom is factorized by the convolution of two atoms selected from two orthogonal factor dictionaries respectively. This factorization scheme enables us to efficiently learn an expressive dictionary with over-completeness and non-rank-one atoms. Based on our convolutional analysis model and factorization scheme, an effective yet efficient dictionary learning method is proposed for visual tensor completion. Extensive experiments show that, our method not only outperforms existing dictionary-based approaches with relatively-low time cost, but also outperforms recent low-rank approaches.
Keywords:
Tensile stress
Dictionaries
Machine learning
Visualization
Convolutional codes
Encoding
Analytical models
Tensor dictionary learning
tensor completion
convolutional sparse coding
factorized dictionary learning
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