SURE based truncated tensor nuclear norm regularization for low rank tensor completion

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Low rank tensor completion aims to recover the underlying low rank tensor obtained from its partial observations, this has a wide range of applications in Signal Processing and Machine Learning. A number of recent low rank tensor methods have successfully utilised the tensor singular value decomposition method with tensor nuclear norm minimisation via tensor singular value thresholding. This approach while proving to be effective has the potential issue that it may over or under shrink the singular values which will effect the overall performance. A truncated nuclear norm based method has been introduced which explicitly exploits the low rank assumption within the optimization in combination with tensor singular value thresholding. In this work the truncated nuclear norm approach is extended to incorporate a data driven approach based on Stein’s unbiased risk estimation method which efficiently thresholds the singular values. Experimental results in a colour image denoising problem demonstrate the efficiency and accuracy of the method.
Original languageEnglish
Title of host publicationProceedings of the 28th European Signal Processing Conference
Number of pages5
ISBN (Print)9789082797053
Publication statusPublished - 18 Dec 2020
Event28th European Signal Processing Conference - Amsterdam, Netherlands
Duration: 18 Jan 202122 Jan 2021


Conference28th European Signal Processing Conference
Abbreviated titleEUSIPCO 2020
Internet address


  • SURE
  • Singular Value Shrinkage
  • Truncated Tensor Nuclear Norm


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