Tensor Denoising Using Low-Rank Tensor Train Decomposition

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Abstract
Exploiting the latent low-rankness of tensors is crucial in tensor denoising. Classically, many methods use the Tucker model to find the low-rank structure of a tensor. Recently, the tensor train (TT) model has drawn wide attention owing to its powerful representation ability and well-balanced matricization scheme for a tensor, and it has been successfully applied to various problems in signal processing and machine learning applications. In this letter, we propose a tensor denoising method using the TT singular value decomposition and information criteria, where we leverage the minimum description length to automatically estimate the TT rank. Furthermore, we establish the relationship between Tucker decomposition and TT decomposition. In specific, the low Tucker rank of a tensor is the sufficient but unnecessary condition to the low TT rank. It unveils in theory the potential advantages of the TT model in characterizing the latent low-rankness of tensor. Denoising experiments on both synthetic data and real HSI dataset demonstrate its superiority against Tucker-based methods.
Funding Information
  • National Key R&D Program of China (2018YFE0207600)
  • National Natural Science Foundation of China (61671046, 61911530216, 61671382, 6196113039, U1834210)
  • Fundamental Research Funds for the Central Universities (2020JBZD005)
  • Natural Science Foundation of Beijing Municipality (4182050)
  • NSFC Outstanding Youth Foundation (61725101)
  • Royal Society Newton Advanced Fellowship (NA191006)

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