Tensor denoising via dual Schatten norms

Denoising is an important preprocessing step that can improve the quality of the data and make it more suitable for further analysis, enhance the performance of machine learning models, identify underlying patterns, reduce computation time, and make data more interpretable by humans. Here we propose...

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Bibliographic Details
Published in:Optimization letters 2024-06, Vol.18 (5), p.1285-1301
Main Author: Bagherian, Maryam
Format: Article
Language:English
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Short Communication
Simulation
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Summary:Denoising is an important preprocessing step that can improve the quality of the data and make it more suitable for further analysis, enhance the performance of machine learning models, identify underlying patterns, reduce computation time, and make data more interpretable by humans. Here we propose a tensor denoising approach based on Pareto efficient pairs and its relation with dual norms. We relate the problem of tensor denoising to that of maximizing the norm of the clean part while minimizing the norm of the noise. We propose a simple efficient method to remove additive noise of signals and compare the results, in terms of PSNR and MSE, with those of standard decomposition-based denoising methods over synthetically generated data.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-023-02068-8