论文标题
稳定的张量主体组件分析：通过确定性模型的精确恢复
Robust Tensor Principal Component Analysis: Exact Recovery via Deterministic Model
论文作者
论文摘要
张量，也称为多维阵列，源自信号处理，制造过程，医疗保健等的许多应用。作为张量文献中最受欢迎的方法之一，可稳定的张量主成分分析（RTPCA）是一种非常有效的工具，可以在张量中提取低级和稀疏组件。在本文中，提出了一种基于最近开发的张量张量产物和张量奇异值分解（T-SVD）的新方法来分析RTPCA。具体而言，它旨在解决一个凸优化问题，该问题的目标函数是张量核标准和L1-norm的加权组合。在RTPCA的大多数文献中，确切的恢复是建立在张量不一致条件和稀疏支撑模型的假设上的。与这种常规方式不同，在本文中，没有任何随机性的假设，可以通过表征张张量的平台不一致来以完全确定的方式实现确切的恢复，这是低秩量张量空间与稀疏张量的模式之间的不确定性原理。
Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component analysis (RTPCA) is a very effective tool to extract the low rank and sparse components in tensors. In this paper, a new method to analyze RTPCA is proposed based on the recently developed tensor-tensor product and tensor singular value decomposition (t-SVD). Specifically, it aims to solve a convex optimization problem whose objective function is a weighted combination of the tensor nuclear norm and the l1-norm. In most of literature of RTPCA, the exact recovery is built on the tensor incoherence conditions and the assumption of a uniform model on the sparse support. Unlike this conventional way, in this paper, without any assumption of randomness, the exact recovery can be achieved in a completely deterministic fashion by characterizing the tensor rank-sparsity incoherence, which is an uncertainty principle between the low-rank tensor spaces and the pattern of sparse tensor.
