张量(固有定义)
K-SVD公司
奇异值分解
计算机科学
模式识别(心理学)
人工智能
算法
数学
秩(图论)
稀疏逼近
组合数学
纯数学
作者
Qilun Luo,Wen Li,Mingqing Xiao
出处
期刊:IEEE transactions on neural networks and learning systems
[Institute of Electrical and Electronics Engineers]
日期:2023-01-01
卷期号:: 1-15
标识
DOI:10.1109/tnnls.2023.3248156
摘要
The recent study on tensor singular value decomposition (t-SVD) that performs the Fourier transform on the tubes of a third-order tensor has gained promising performance on multidimensional data recovery problems. However, such a fixed transformation, e.g., discrete Fourier transform and discrete cosine transform, lacks being self-adapted to the change of different datasets, and thus, it is not flexible enough to exploit the low-rank and sparse property of the variety of multidimensional datasets. In this article, we consider a tube as an atom of a third-order tensor and construct a data-driven learning dictionary from the observed noisy data along the tubes of the given tensor. Then, a Bayesian dictionary learning (DL) model with tensor tubal transformed factorization, aiming to identify the underlying low-tubal-rank structure of the tensor effectively via the data-adaptive dictionary, is developed to solve the tensor robust principal component analysis (TRPCA) problem. With the defined pagewise tensor operators, a variational Bayesian DL algorithm is established and updates the posterior distributions instantaneously along the third dimension to solve the TPRCA. Extensive experiments on real-world applications, such as color image and hyperspectral image denoising and background/foreground separation problems, demonstrate both effectiveness and efficiency of the proposed approach in terms of various standard metrics.
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