矩阵分解方法应用研究进展

Review of matrix decomposition methods application

  • 摘要: 近年来,采用矩阵分解方法对高维、异构、海量的遥感图像数据进行挖掘与重建的研究工作被不断报道. 回顾了2000年以来国内外矩阵分解方法应用研究的最新进展,主要包括:矩阵分解方法及其重要改进与应用研究进展;基于矩阵分解的数据重建与特征挖掘方法研究态势;矩阵分解方法在遥感图像重建领域面临的挑战. 结果表明,近20年来相关研究总体呈现逐渐增多的趋势,研究重点从传统矩阵分解方法转向高光谱图像分析、图像重建、低秩高效分解方法以及稀疏特征挖掘等方面,稀疏矩阵分解、概率矩阵分解、非负矩阵分解的研究工作占比逐年递增,其中,地理、遥感、生态学等领域的应用研究最为活跃; 非负矩阵分解方法具有良好的图像特征挖掘能力,有望实现卫星遥感图像在低秩水平下地表信息的完整重建,利用矩阵分解方法从遥感图像特征并重建图像数据具备良好的可行性和潜力.

     

    Abstract: In recent years, the research work on mining and reconstruction of high-dimensional, heterogeneous, and massive remote sensing image data using matrix decomposition methods has been reported continuously. In this paper, we review the cutting edge of matrix decomposition application in both domestic and international studies since 2000, focusing primarily on the progress of matrix decomposition, its key improvements and application optimizations; the research trends in data reconstruction and feature mining methods based on matrix decomposition; and the challenges faced by matrix decomposition methods in the field of remote sensing image reconstruction. The results indicate that over the past 20 years, the related research has shown a gradual increase in volume, with a shift in focus from traditional decomposition methods to hyperspectral image analysis, image reconstruction, low-rank efficiency decomposition methods, and sparse feature mining. The proportion of research on sparse matrix decomposition, probabilistic matrix decomposition, and non-negative matrix decomposition increased year by year, with the most active application research in the fields of geography, remote sensing, and ecology. The non-negative matrix decomposition method exhibits strong capabilities in image feature mining and is anticipated to achieve complete reconstruction of surface information from satellite remote sensing images at low-rank levels. Utilizing matrix decomposition methods to extract features and reconstruct image data from remote sensing images demonstrates both feasibility and significant potential for further expansion.

     

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