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    New coupled nonlinear transforms (CoNoT) improve tensor completion by treating spatial and spectral modes differently. This approach, using convolutional neural networks (CNNs), enhances low-rank approximation for multidimensional image completion.

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    Area of Science:

    • Multidimensional data analysis
    • Machine learning for image processing

    Background:

    • Transform-based tensor nuclear norm (TNN) methods are popular for tensor completion (TC).
    • Existing TNN methods often treat tensor modes (spatial, spectral/temporal) uniformly, neglecting their distinct characteristics.
    • This uniform treatment can limit the effectiveness of low-rank approximation in capturing underlying data structures.

    Purpose of the Study:

    • To introduce a novel low-rank tensor representation using coupled nonlinear transforms (CoNoT).
    • To address the limitations of TNN methods by exploiting differential mode characteristics for improved low-rank approximation.
    • To develop advanced multidimensional image completion models based on this new representation.

    Main Methods:

    • Developed a coupled nonlinear transform (CoNoT) utilizing convolutional neural networks (CNNs).
    • CoNoT learns spatial and spectral/temporal transforms separately and couples them to enhance low-rank structure.
    • Proposed an enhanced version (Ms-CoNoT) to incorporate spatial multiscale properties.
    • Implemented unsupervised learning of CoNoT directly from observed multidimensional image data.

    Main Results:

    • The proposed CoNoT-based models demonstrate superior performance in multidimensional image completion compared to state-of-the-art methods.
    • Both qualitative and quantitative experimental results on real-world data validate the effectiveness of the new approach.
    • The Ms-CoNoT variant further enhances performance by leveraging spatial multiscale information.

    Conclusions:

    • The coupled nonlinear transform (CoNoT) offers a more effective approach to low-rank tensor representation for multidimensional data.
    • The developed image completion models significantly outperform existing methods, particularly for real-world data.
    • The findings highlight the importance of considering mode-specific traits and multiscale properties in tensor completion.