基于空谱先验与高阶张量表示的超分辨率重建算法

doi:10.19678/j.issn.1000-3428.0069092

计算机工程 ›› 2025, Vol. 51 ›› Issue (9): 220-230. doi: 10.19678/j.issn.1000-3428.0069092

基于空谱先验与高阶张量表示的超分辨率重建算法

王震¹^,²^,³, 陈希爱²^,³^,*(), 杨超¹^,²^,³, 贾慧迪²^,³^,⁴, 韩志²^,³, 唐延东²^,³

1. 沈阳化工大学信息工程学院, 辽宁沈阳 110142
2. 中国科学院沈阳自动化研究所机器人学国家重点实验室，辽宁沈阳 110016
3. 中国科学院机器人与智能制造创新研究院，辽宁沈阳 110016
4. 中国科学院大学，北京 100049

收稿日期:2023-12-25 修回日期:2024-04-23 出版日期:2025-09-15 发布日期:2025-09-26
通讯作者: 陈希爱
基金资助:
国家自然科学基金(61821005); 中国科学院稳定支持基础研究领域青年团队计划(YSBR-041); 中国科学院青年创新促进会(2022196)

Super-Resolution Reconstruction Algorithm Based on Spatial-Spectral Prior and High-Order Tensor Representation

WANG Zhen¹^,²^,³, CHEN Xi′ai²^,³^,*(), YANG Chao¹^,²^,³, JIA Huidi²^,³^,⁴, HAN Zhi²^,³, TANG Yandong²^,³

1. College of Information Engineering, Shenyang University of Chemical Technology, Shenyang 110142, Liaoning, China
2. State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China
3. Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016, Liaoning, China
4. University of Chinese Academy of Sciences, Beijing 100049, China

Received:2023-12-25 Revised:2024-04-23 Online:2025-09-15 Published:2025-09-26
Contact: CHEN Xi′ai

摘要/Abstract

摘要：

现有高光谱图像(HIS)超分辨率任务存在信息表示不充分、先验信息利用不足、重建精度不高的问题，严重影响后续图像处理任务精度。针对此问题，提出基于多-高光谱图像融合的非局部高阶张量表示算法，用于HSI超分辨率重建。通过k-means算法将图像划分为非局部相似块，将其构建成高阶张量，并利用张量火车所具有的均衡分解策略挖掘非局部高阶张量空间-光谱低秩冗余性。由于图像空间域中具有局部平滑特性，因此采用加权组稀疏正则项描述此特征，并构造加权光谱解混约束项来解决超分辨过程中光谱数据的融合失真问题，利用交替方向乘子法推导给出各变量具体求解计算过程。在公开的3个真实数据集CAVE、Pavia University、Indian Pines上的实验结果表明，与现有代表性超分辨率算法相比，所提算法的平均峰值信噪比(PSNR)和结构相似性(SSIM)分别提高0.290 8 dB、0.002，光谱角映射器(SAM)和全局相对误差指数分别降低了0.116°和3.1%。

关键词: 超分辨率, 融合, 非局部高阶张量, 张量火车, 光谱解混

Abstract:

Existing Hyper-Spectral Image (HSI) super-resolution tasks suffer from issues such as inadequate information representation, limited utilization of prior knowledge, and low reconstruction accuracy. These problems significantly affect the accuracy of subsequent image-processing tasks. To address this challenge, this study proposes a HSI super-resolution reconstruction algorithm based on spatial-spectral prior and high-order tensor representation. The algorithm divides image into non-local similar blocks using the k-means algorithm and constructs them into high-order tensors. The balanced decomposition strategy of the tensor-train is used to exploit the low-rank redundancy in these non-local high-order tensors. In addition, considering the local smoothness property in the image spatial domain, a weighted group sparse regularization term is employed. Furthermore, a weighted spectral unmixing constraint term is used to address fusion distortion issues in spectral data during processes, and the calculation process for each variable is presented using the alternating direction method of multipliers. In experimental evaluations on three publicly available real datasets—CAVE, Pavia University, and Indian Pines, the proposed algorithm improves the average Peak-Signal-to-Noise-Ratio (PSNR), Structural Similarity Index (SSIM) by 0.290 8 dB, 0.002, Spectral Angle Mapper (SAM) and global relative error index are reduced by 0.116° and 3.1%, respectively.

Key words: super-resolution, fusion, non-local high-order tensor, tensor-train, spectral unmixing

王震, 陈希爱, 杨超, 贾慧迪, 韩志, 唐延东. 基于空谱先验与高阶张量表示的超分辨率重建算法[J]. 计算机工程, 2025, 51(9): 220-230.

WANG Zhen, CHEN Xi′ai, YANG Chao, JIA Huidi, HAN Zhi, TANG Yandong. Super-Resolution Reconstruction Algorithm Based on Spatial-Spectral Prior and High-Order Tensor Representation[J]. Computer Engineering, 2025, 51(9): 220-230.

https://www.ecice06.com/CN/Y2025/V51/I9/220

图/表 14

图1 所提算法的总框架

Fig.1 General framework of the proposed algorithm

图2 在数据集中不同场景的彩色图像

Fig.2 The color images of different scenes in datasets

图3 不同方法重构后的CD图像细节展示

Fig.3 Detail show of CD images after reconstruction by different methods

图4 不同方法重构后的CAVE图像

Fig.4 CAVE images after reconstruction by different methods

图5 不同方法重构后的Pavia University图像

Fig.5 Pavia University images after by different methods

图6 不同方法重构后的Indian Pines图像

Fig.6 Indian Pines images after reconstruction by different methods

图7 不同方法重构的Balloons，Pavia University，Indian Pines数据每个波段的PSNR值

Fig.7 The PSNR values of each band of Balloons, Pavia University and Indian Pines datas reconstructed by different methods

图8 消融实验的结果图

Fig.8 Results images of ablation experiment

图9 聚类数对结果的影响

Fig.9 The effect of cluster number on the results

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