张量低秩建模及其在信号处理中的应用
Tensor Low Rank Modeling and Its Applications in Signal Processing
摘要：
使用张量建模多维信号比将其表示为矩阵的集合更有说服力。基于张量的方法可以探索多维信号的丰富的空间和时间结构。这种建模的支柱是张量代数的数学基础。基于线性变换的张量代数构造了低复杂度、高性能的代数结构，适合于多维信号的自检测。从信号处理的角度对基于线性变换的张量代数进行了全面的介绍。多维信号的秩是一个宝贵的属性，它可以让我们深入了解它的结构方面。所有自然的多维信号都可以近似为一个低秩信号，而不会丢失重要信息。低秩近似在许多信号处理应用中是有益的，诸如去噪、缺失样本估计、分辨率增强、分类、背景估计、目标检测、风化、聚类以及更多的应用。文中还详细介绍了低秩建模在上述信号处理应用中的方法和手段。
英文摘要：
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The backbone of this modeling is the mathematical foundations of tensor algebra. The linear transform based tensor algebra furnishes low complex and high performance algebraic structures suitable for the introspection of the multidimensional signal. A comprehensive introduction of the linear transform based tensor algebra is provided from the signal processing viewpoint. The rank of a multidimensional signal is a precious property which gives an insight into the structural aspects of it. All natural multidimensional signals can be approximated to a low rank signal without losing significant information. The low rank approximation is beneficial in many signal processing applications such as denoising, missing sample estimation, resolution enhancement, classification, background estimation, object detection, deweathering, clustering and much more applications. Detailed case study of the ways and means of the low rank modeling in the above said signal processing applications are also presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
