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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (6): 1021-1040.doi: 10.3969/j.issn.1005-3085.2024.06.003

• • 上一篇    下一篇

超光谱图像数据中的正则化张量补全算法

谢亚君1,2   

  1. 1. 福州外语外贸学院大数据学院，福州 350202
    2. 福州外语外贸学院智能计算与数字科技重点实验室，福州 350202
  • 收稿日期:2022-03-28 接受日期:2022-12-25 出版日期:2024-12-15 发布日期:2024-12-15
  • 基金资助:
    福建省自然科学基金 (2022J01378; 2023J011127)；福建省重大教改项目 (FBJG20200310)；新工科项目 (J1593419745784GS).

Regularization Tensor Completion Algorithm for Hyperspectral Image Data

XIE Yajun1,2   

  1. 1. School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202
    2. Key Laboratory of Intelligent Computing and Digital Technology, Fuzhou University of International Studies and Trade, Fuzhou 350202
  • Received:2022-03-28 Accepted:2022-12-25 Online:2024-12-15 Published:2024-12-15
  • Supported by:
    The Natural Science Foundation of Fujian Province (2022J01378; 2023J011127); the Major Educational Reform Project of Fujian Province (FBJG20200310); the New Engineering Project (J1593419745784GS).

摘要：

数字图像的高效处理技术被广泛应用于大数据和人工智能各个领域，尤其是超光谱图像处理问题，目前已成为学术研究的热点。超光谱图像数据常以高维数组形式存储，然而常用的高维数组矩阵化方法因无法准确诠释其内部结构而缺乏泛化能力。提出了一个新的张量补全算法来重构超光谱图像并进行相应数据分析。首先，建立一个适合超光谱数据处理的带正则项的张量核范数优化模型。其次，针对所构造的张量优化模型，提出一个高效的变参数交替方向多乘子算法进行求解，并建立算法的收敛性理论。最后，通过与当前一些有效的算法进行多维度比较与分析，验证算法的可行性和有效性。

关键词: 超光谱图像, 张量补全, 正则化, 交替方向乘子法, 变参策略

Abstract:

The efficient digital image processing technology is widely used in the fields of big data and artificial intelligence, especially hyperspectral image processing, which has become a hot topic in academic research. Hyperspectral data are usually stored in the form of high-dimensional arrays. However, the matrixization method of high-dimensional arrays lacks generalization ability as its internal structure cannot be accurately interpreted. In this paper, a novel tensor completion algorithm is proposed to reconstruct hyperspectral image and analyze the corresponding data. Firstly, a tensor kernel norm optimization model with regularization is established for hyperspectral image processing. Secondly, a new multi-multiplier algorithm with variable parameter alternating-direction is proposed to solve the tensor optimization model, and the convergence theory is established. Finally, the feasibility and effectiveness of the algorithm are verified by multi-dimensional comparison and analysis with some current effective algorithms.

Key words: hyperspectral image, tensor completion, regularization, alternating direction me-thodr of multipliers, strategy of variable parameter

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