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<p>In hyperspectral-multispectral image fusion, tensor ring (TR) decomposition has attracted considerable attention due to its strong capability to capture intrinsic structural characteristics of high-dimensional data. However, it remains challenging to effectively impose low-rank constraints on the TR factors while preserving spatial smoothness. Existing methods typically treat low-rankness and smoothness priors as separate regularization terms, neglecting their synergistic interaction. To address this issue, this paper proposes a joint factor smoothed logarithmic tensor nuclear norm (JFSLTNN) method under the TR decomposition framework, which integrates the weighted total variation and the logarithmic tensor nuclear norm (LTNN) into a unified regularizer. Specifically, spatial smoothness is enhanced by computing the weighted gradient of the TR factors along the second mode, while a more accurate low-rank approximation is achieved by applying the mode-2 LTNN to the weighted gradient tensor. This design not only reduces the number of parameters, but also enhances fusion performance. Furthermore, an efficient proximal alternating minimization algorithm is developed to solve the proposed model. Experiments on two datasets demonstrate that the proposed method outperforms existing state-of-the-art approaches in both visual quality and quantitative metrics, validating its superior performance. The source code is publicly available at: <a href="https://github.com/MenglingHe1/JFSLTNN.git">https://github.com/MenglingHe1/JFSLTNN.git</a>.</p>

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JFSLTNN: a joint factor smoothed log-nuclear norm tensor regularization for hyperspectral image fusion under tensor ring decomposition

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Mengling He,
  • Jun Zhang

摘要

In hyperspectral-multispectral image fusion, tensor ring (TR) decomposition has attracted considerable attention due to its strong capability to capture intrinsic structural characteristics of high-dimensional data. However, it remains challenging to effectively impose low-rank constraints on the TR factors while preserving spatial smoothness. Existing methods typically treat low-rankness and smoothness priors as separate regularization terms, neglecting their synergistic interaction. To address this issue, this paper proposes a joint factor smoothed logarithmic tensor nuclear norm (JFSLTNN) method under the TR decomposition framework, which integrates the weighted total variation and the logarithmic tensor nuclear norm (LTNN) into a unified regularizer. Specifically, spatial smoothness is enhanced by computing the weighted gradient of the TR factors along the second mode, while a more accurate low-rank approximation is achieved by applying the mode-2 LTNN to the weighted gradient tensor. This design not only reduces the number of parameters, but also enhances fusion performance. Furthermore, an efficient proximal alternating minimization algorithm is developed to solve the proposed model. Experiments on two datasets demonstrate that the proposed method outperforms existing state-of-the-art approaches in both visual quality and quantitative metrics, validating its superior performance. The source code is publicly available at: https://github.com/MenglingHe1/JFSLTNN.git.